Hidden sectors in string theory: kinetic mixings, fifth forces and quintessence

  • Bobby Samir Acharya
  • Anshuman Maharana
  • Francesco MuiaEmail author
Open Access
Regular Article - Theoretical Physics


Light moduli fields in string compactifications can have interesting implications for particle physics and cosmology. Fifth force bounds impose stringent constraints on the interactions of such moduli with the visible sector. To be consistent with the bounds, they need to be part of hidden sectors which interact with the Standard Model with weaker-than-Planck suppressed interactions. We consider scenarios in which the visible sector degrees of freedom are localised in the compactification and light moduli arise as closed string degrees of freedom associated with hidden sectors which are geometrically separated (in the extra-dimensions) from the Standard Model. Kinetic mixings lead to interactions between the moduli and the visible sector — we compute these using Kähler potentials of string/M-theory compactifications. We argue that in general these interactions provide a lower bound on the strength of the interactions between the moduli and the visible sector. The interactions scale with inverse powers of the volume of the compactification, thus fifth force bounds can be translated to lower bounds on the volume of the extra-dimensions. We find that compactification volumes have to be large to evade the bounds. This imposes interesting constraints on quintessence model building in string theory. Our results for the strength of the interactions can also be used to quantify the fine-tuning necessary for the stability of the potential of a light modulus against quantum corrections involving visible sector loops.


Phenomenology of Large extra dimensions Strings and branes phenomenology 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


  1. [1]
    C.M. Will, The confrontation between general relativity and experiment, Living Rev. Rel. 17 (2014) 4 [arXiv:1403.7377] [INSPIRE].zbMATHGoogle Scholar
  2. [2]
    E.G. Adelberger, B.R. Heckel and A.E. Nelson, Tests of the gravitational inverse square law, Ann. Rev. Nucl. Part. Sci. 53 (2003) 77 [hep-ph/0307284] [INSPIRE].
  3. [3]
    G.D. Coughlan et al., Cosmological problems for the Polonyi potential, Phys. Lett. B 131 (1983) 59.ADSGoogle Scholar
  4. [4]
    T. Banks, D.B. Kaplan and A.E. Nelson, Cosmological implications of dynamical supersymmetry breaking, Phys. Rev. D 49 (1994) 779 [hep-ph/9308292] [INSPIRE].
  5. [5]
    B. de Carlos, J.A. Casas, F. Quevedo and E. Roulet, Model independent properties and cosmological implications of the dilaton and moduli sectors of 4D strings, Phys. Lett. B 318 (1993) 447 [hep-ph/9308325] [INSPIRE].
  6. [6]
    G. Kane, K. Sinha and S. Watson, Cosmological moduli and the post-inflationary universe: a critical review, Int. J. Mod. Phys. D 24 (2015) 1530022 [arXiv:1502.07746] [INSPIRE].ADSMathSciNetGoogle Scholar
  7. [7]
    B.S. Acharya et al., Non-thermal dark matter and the moduli problem in string frameworks, JHEP 06 (2008) 064 [arXiv:0804.0863] [INSPIRE].ADSGoogle Scholar
  8. [8]
    G. Kane, J. Shao, S. Watson and H.-B. Yu, The baryon-dark matter ratio via moduli decay after Affleck-Dine baryogenesis, JCAP 11 (2011) 012 [arXiv:1108.5178] [INSPIRE].ADSGoogle Scholar
  9. [9]
    R. Allahverdi, M. Cicoli, B. Dutta and K. Sinha, Correlation between dark matter and dark radiation in string compactifications, JCAP 10 (2014) 002 [arXiv:1401.4364] [INSPIRE].ADSGoogle Scholar
  10. [10]
    R. Easther, R. Galvez, O. Ozsoy and S. Watson, Supersymmetry, nonthermal dark matter and precision cosmology, Phys. Rev. D 89 (2014) 023522 [arXiv:1307.2453] [INSPIRE].ADSGoogle Scholar
  11. [11]
    K. Dutta and A. Maharana, Inflationary constraints on modulus dominated cosmology, Phys. Rev. D 91 (2015) 043503 [arXiv:1409.7037] [INSPIRE].ADSGoogle Scholar
  12. [12]
    L. Aparicio et al., Non-thermal CMSSM with a 125 GeV Higgs, JHEP 05 (2015) 098 [arXiv:1502.05672] [INSPIRE].ADSGoogle Scholar
  13. [13]
    R. Allahverdi, M. Cicoli and F. Muia, Affleck-Dine baryogenesis in type IIB string models, JHEP 06 (2016) 153 [arXiv:1604.03120] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  14. [14]
    R. Allahverdi, K. Dutta and A. Maharana, Constraining non-thermal dark matter by CMB, JCAP 10 (2018) 038 [arXiv:1808.02659] [INSPIRE].ADSGoogle Scholar
  15. [15]
    S. Antusch et al., Oscillons from string moduli, JHEP 01 (2018) 083 [arXiv:1708.08922] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  16. [16]
    M.A. Amin, J. Fan, K.D. Lozanov and M. Reece, Cosmological dynamics of Higgs potential fine tuning, Phys. Rev. D 99 (2019) 035008 [arXiv:1802.00444] [INSPIRE].Google Scholar
  17. [17]
    S. Krippendorf, F. Muia and F. Quevedo, Moduli stars, JHEP 08 (2018) 070 [arXiv:1806.04690] [INSPIRE].ADSMathSciNetGoogle Scholar
  18. [18]
    B. Jain and J. Khoury, Cosmological tests of gravity, Annals Phys. 325 (2010) 1479 [arXiv:1004.3294] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  19. [19]
    T. Damour and J.F. Donoghue, Equivalence principle violations and couplings of a light dilaton, Phys. Rev. D 82 (2010) 084033 [arXiv:1007.2792] [INSPIRE].ADSGoogle Scholar
  20. [20]
    P. Touboul et al., MICROSCOPE mission: first results of a space test of the equivalence principle, Phys. Rev. Lett. 119 (2017) 231101 [arXiv:1712.01176] [INSPIRE].ADSGoogle Scholar
  21. [21]
    J. Bergé et al., MICROSCOPE mission: first constraints on the violation of the weak equivalence principle by a light scalar dilaton, Phys. Rev. Lett. 120 (2018) 141101 [arXiv:1712.00483] [INSPIRE].ADSGoogle Scholar
  22. [22]
    T.A. Wagner, S. Schlamminger, J.H. Gundlach and E.G. Adelberger, Torsion-balance tests of the weak equivalence principle, Class. Quant. Grav. 29 (2012) 184002 [arXiv:1207.2442] [INSPIRE].ADSGoogle Scholar
  23. [23]
    A.M. Nobili and A. Anselmi, Testing the equivalence principle in space after the MICROSCOPE mission, Phys. Rev. D 98 (2018) 042002 [arXiv:1803.03313] [INSPIRE].ADSGoogle Scholar
  24. [24]
    J. Giedt, Completion of standard model like embeddings, Annals Phys. 289 (2001) 251 [hep-th/0009104] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  25. [25]
    M. Cvetič, T. Li and T. Liu, Supersymmetric patiSalam models from intersecting D6-branes: a road to the standard model, Nucl. Phys. B 698 (2004) 163 [hep-th/0403061] [INSPIRE].ADSzbMATHGoogle Scholar
  26. [26]
    W. Taylor and Y.-N. Wang, A Monte Carlo exploration of threefold base geometries for 4d F-theory vacua, JHEP 01 (2016) 137 [arXiv:1510.04978] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  27. [27]
    B.S. Acharya et al., The lightest visible-sector supersymmetric particle is likely to be unstable, Phys. Rev. Lett. 117 (2016) 181802 [arXiv:1604.05320] [INSPIRE].ADSGoogle Scholar
  28. [28]
    B.S. Acharya et al., Categorisation and detection of dark matter candidates from string/M-theory hidden sectors, JHEP 09 (2018) 130 [arXiv:1707.04530] [INSPIRE].ADSGoogle Scholar
  29. [29]
    S. Kachru, R. Kallosh, A.D. Linde and S.P. Trivedi, De Sitter vacua in string theory, Phys. Rev. D 68 (2003) 046005 [hep-th/0301240] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  30. [30]
    F. Denef, M.R. Douglas and B. Florea, Building a better racetrack, JHEP 06 (2004) 034 [hep-th/0404257] [INSPIRE].ADSMathSciNetGoogle Scholar
  31. [31]
    F. Denef et al., Fixing all moduli in a simple F-theory compactification, Adv. Theor. Math. Phys. 9 (2005) 861 [hep-th/0503124] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  32. [32]
    D. Lüst, S. Reffert, W. Schulgin and S. Stieberger, Moduli stabilization in type IIB orientifolds (I): orbifold limits, Nucl. Phys. B 766 (2007) 68 [hep-th/0506090] [INSPIRE].ADSzbMATHGoogle Scholar
  33. [33]
    D. Lüst et al., Moduli stabilization in type IIB orientifolds (II), Nucl. Phys. B 766 (2007) 178 [hep-th/0609013] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  34. [34]
    V. Balasubramanian, P. Berglund, J.P. Conlon and F. Quevedo, Systematics of moduli stabilisation in Calabi-Yau flux compactifications, JHEP 03 (2005) 007 [hep-th/0502058] [INSPIRE].ADSMathSciNetGoogle Scholar
  35. [35]
    M. Cicoli et al., Explicit de Sitter flux vacua for global string models with chiral matter, JHEP 05 (2014) 001 [arXiv:1312.0014] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  36. [36]
    A. Westphal, De Sitter string vacua from Kähler uplifting, JHEP 03 (2007) 102 [hep-th/0611332] [INSPIRE].ADSzbMATHGoogle Scholar
  37. [37]
    J. Louis, M. Rummel, R. Valandro and A. Westphal, Building an explicit de Sitter, JHEP 10 (2012) 163 [arXiv:1208.3208] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  38. [38]
    M. Rummel and A. Westphal, A sufficient condition for de Sitter vacua in type IIB string theory, JHEP 01 (2012) 020 [arXiv:1107.2115] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  39. [39]
    A.P. Braun, M. Rummel, Y. Sumitomo and R. Valandro, De Sitter vacua from a D-term generated racetrack potential in hypersurface Calabi-Yau compactifications, JHEP 12 (2015) 033 [arXiv:1509.06918] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  40. [40]
    D. Gallego, M.C.D. Marsh, B. Vercnocke and T. Wrase, A new class of de Sitter vacua in type IIB large volume compactifications, JHEP 10 (2017) 193 [arXiv:1707.01095] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  41. [41]
    K. Dasgupta, G. Rajesh and S. Sethi, M theory, orientifolds and G-flux, JHEP 08 (1999) 023 [hep-th/9908088] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  42. [42]
    S. Gukov, C. Vafa and E. Witten, CFT’s from Calabi-Yau four folds, Nucl. Phys. B 584 (2000) 69 [Erratum ibid. B 608 (2001) 477] [hep-th/9906070] [INSPIRE].
  43. [43]
    R. Bousso and J. Polchinski, Quantization of four form fluxes and dynamical neutralization of the cosmological constant, JHEP 06 (2000) 006 [hep-th/0004134] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  44. [44]
    J.L. Feng, J. March-Russell, S. Sethi and F. Wilczek, Saltatory relaxation of the cosmological constant, Nucl. Phys. B 602 (2001) 307 [hep-th/0005276] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  45. [45]
    S.B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66 (2002) 106006 [hep-th/0105097] [INSPIRE].ADSMathSciNetGoogle Scholar
  46. [46]
    B.S. Acharya et al., An M-theory solution to the hierarchy problem, Phys. Rev. Lett. 97 (2006) 191601 [hep-th/0606262] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  47. [47]
    B. Dundee, S. Raby and A. Westphal, Moduli stabilization and SUSY breaking in heterotic orbifold string models, Phys. Rev. D 82 (2010) 126002 [arXiv:1002.1081] [INSPIRE].ADSGoogle Scholar
  48. [48]
    S.L. Parameswaran, S. Ramos-Sanchez and I. Zavala, On moduli stabilisation and de Sitter vacua in MSSM heterotic orbifolds, JHEP 01 (2011) 071 [arXiv:1009.3931] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  49. [49]
    A. Font, L.E. Ibáñez, D. Lüst and F. Quevedo, Supersymmetry breaking from duality invariant gaugino condensation, Phys. Lett. B 245 (1990) 401 [INSPIRE].ADSMathSciNetGoogle Scholar
  50. [50]
    S. Ferrara, N. Magnoli, T.R. Taylor and G. Veneziano, Duality and supersymmetry breaking in string theory, Phys. Lett. B 245 (1990) 409 [INSPIRE].ADSMathSciNetGoogle Scholar
  51. [51]
    H.P. Nilles and M. Olechowski, Gaugino condensation and duality invariance, Phys. Lett. B 248 (1990) 268 [INSPIRE].ADSGoogle Scholar
  52. [52]
    J.A. Casas, Z. Lalak, C. Muñoz and G.G. Ross, Hierarchical supersymmetry breaking and dynamical determination of compactification parameters by nonperturbative effects, Nucl. Phys. B 347 (1990) 243 [INSPIRE].ADSGoogle Scholar
  53. [53]
    B. de Carlos, J.A. Casas and C. Muñoz, Supersymmetry breaking and determination of the unification gauge coupling constant in string theories, Nucl. Phys. B 399 (1993) 623 [hep-th/9204012] [INSPIRE].ADSGoogle Scholar
  54. [54]
    R. Blumenhagen, G. Honecker and T. Weigand, Loop-corrected compactifications of the heterotic string with line bundles, JHEP 06 (2005) 020 [hep-th/0504232] [INSPIRE].ADSMathSciNetGoogle Scholar
  55. [55]
    L.B. Anderson, J. Gray, A. Lukas and B. Ovrut, Stabilizing all geometric moduli in heterotic Calabi-Yau vacua, Phys. Rev. D 83 (2011) 106011 [arXiv:1102.0011] [INSPIRE].ADSzbMATHGoogle Scholar
  56. [56]
    M. Cicoli, S. de Alwis and A. Westphal, Heterotic moduli stabilisation, JHEP 10 (2013) 199 [arXiv:1304.1809] [INSPIRE].ADSGoogle Scholar
  57. [57]
    E. Silverstein, Simple de Sitter solutions, Phys. Rev. D 77 (2008) 106006 [arXiv:0712.1196] [INSPIRE].ADSMathSciNetGoogle Scholar
  58. [58]
    U.H. Danielsson, P. Koerber and T. Van Riet, Universal de Sitter solutions at tree-level, JHEP 05 (2010) 090 [arXiv:1003.3590] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  59. [59]
    E. Palti, G. Tasinato and J. Ward, WEAKLY-coupled IIA flux compactifications, JHEP 06 (2008) 084 [arXiv:0804.1248] [INSPIRE].ADSMathSciNetGoogle Scholar
  60. [60]
    U.H. Danielsson, S.S. Haque, G. Shiu and T. Van Riet, Towards classical de Sitter solutions in string theory, JHEP 09 (2009) 114 [arXiv:0907.2041] [INSPIRE].ADSMathSciNetGoogle Scholar
  61. [61]
    O. DeWolfe, A. Giryavets, S. Kachru and W. Taylor, Type IIA moduli stabilization, JHEP 07 (2005) 066 [hep-th/0505160] [INSPIRE].ADSMathSciNetGoogle Scholar
  62. [62]
    A. Maloney, E. Silverstein and A. Strominger, De Sitter space in noncritical string theory, hep-th/0205316 [INSPIRE].
  63. [63]
    K. Choi, String or M-theory axion as a quintessence, Phys. Rev. D 62 (2000) 043509 [hep-ph/9902292] [INSPIRE].
  64. [64]
    N. Kaloper and L. Sorbo, Where in the string landscape is quintessence, Phys. Rev. D 79 (2009) 043528 [arXiv:0810.5346] [INSPIRE].ADSGoogle Scholar
  65. [65]
    S. Panda, Y. Sumitomo and S.P. Trivedi, Axions as quintessence in string theory, Phys. Rev. D 83 (2011) 083506 [arXiv:1011.5877] [INSPIRE].ADSGoogle Scholar
  66. [66]
    M. Cicoli, F.G. Pedro and G. Tasinato, Natural quintessence in string theory, JCAP 07 (2012) 044 [arXiv:1203.6655] [INSPIRE].ADSGoogle Scholar
  67. [67]
    Y. Olguin-Trejo, S.L. Parameswaran, G. Tasinato and I. Zavala, Runaway quintessence, out of the swampland, JCAP 01 (2019) 031 [arXiv:1810.08634] [INSPIRE].ADSGoogle Scholar
  68. [68]
    M. Emelin and R. Tatar, Axion hilltops, Kähler modulus quintessence and the swampland criteria, arXiv:1811.07378 [INSPIRE].
  69. [69]
    G. Obied, H. Ooguri, L. Spodyneiko and C. Vafa, De Sitter space and the swampland, arXiv:1806.08362 [INSPIRE].
  70. [70]
    T. Banks, The top 10500 reasons not to believe in the landscape, arXiv:1208.5715 [INSPIRE].
  71. [71]
    I. Bena, M. Graña and N. Halmagyi, On the existence of meta-stable vacua in Klebanov-Strassler, JHEP 09 (2010) 087 [arXiv:0912.3519] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  72. [72]
    I. Bena, M. Graña, S. Kuperstein and S. Massai, Anti-D3 branes: singular to the bitter end, Phys. Rev. D 87 (2013) 106010 [arXiv:1206.6369] [INSPIRE].ADSGoogle Scholar
  73. [73]
    J. Moritz, A. Retolaza and A. Westphal, Toward de Sitter space from ten dimensions, Phys. Rev. D 97 (2018) 046010 [arXiv:1707.08678] [INSPIRE].ADSMathSciNetGoogle Scholar
  74. [74]
    S. Sethi, Supersymmetry breaking by fluxes, JHEP 10 (2018) 022 [arXiv:1709.03554] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  75. [75]
    U.H. Danielsson and T. Van Riet, What if string theory has no de Sitter vacua?, Int. J. Mod. Phys. D 27 (2018) 1830007 [arXiv:1804.01120] [INSPIRE].ADSMathSciNetGoogle Scholar
  76. [76]
    M. Cicoli et al., De Sitter vs. quintessence in string theory, Fortsch. Phys. 67 (2019) 1800079 [arXiv:1808.08967] [INSPIRE].
  77. [77]
    S. Kachru and S.P. Trivedi, A comment on effective field theories of flux vacua, Fortsch. Phys. 67 (2019) 1800086 [arXiv:1808.08971] [INSPIRE].Google Scholar
  78. [78]
    R. Kallosh, A. Linde, E. McDonough and M. Scalisi, De Sitter vacua with a nilpotent superfield, Fortsch. Phys. 67 (2019) 1800068 [arXiv:1808.09428] [INSPIRE].Google Scholar
  79. [79]
    Y. Akrami, R. Kallosh, A. Linde and V. Vardanyan, The landscape, the swampland and the era of precision cosmology, Fortsch. Phys. 67 (2019) 1800075 [arXiv:1808.09440] [INSPIRE].Google Scholar
  80. [80]
    P. Agrawal, G. Obied, P.J. Steinhardt and C. Vafa, On the cosmological implications of the string swampland, Phys. Lett. B 784 (2018) 271 [arXiv:1806.09718] [INSPIRE].ADSGoogle Scholar
  81. [81]
    G. Dvali and C. Gomez, On exclusion of positive cosmological constant, Fortsch. Phys. 67 (2019) 1800092 [arXiv:1806.10877] [INSPIRE].Google Scholar
  82. [82]
    D. Andriot, On the de Sitter swampland criterion, Phys. Lett. B 785 (2018) 570 [arXiv:1806.10999] [INSPIRE].ADSzbMATHGoogle Scholar
  83. [83]
    S. Banerjee et al., Emergent de Sitter cosmology from decaying Anti-de Sitter space, Phys. Rev. Lett. 121 (2018) 261301 [arXiv:1807.01570] [INSPIRE].ADSGoogle Scholar
  84. [84]
    A. Achúcarro and G.A. Palma, The string swampland constraints require multi-field inflation, JCAP 02 (2019) 041 [arXiv:1807.04390] [INSPIRE].ADSGoogle Scholar
  85. [85]
    S.K. Garg and C. Krishnan, Bounds on slow roll and the de Sitter swampland, arXiv:1807.05193 [INSPIRE].
  86. [86]
    A. Kehagias and A. Riotto, A note on inflation and the swampland, Fortsch. Phys. 66 (2018) 1800052 [arXiv:1807.05445] [INSPIRE].MathSciNetGoogle Scholar
  87. [87]
    M. Dias, J. Frazer, A. Retolaza and A. Westphal, Primordial gravitational waves and the swampland, Fortsch. Phys. 67 (2019) 1800063 [arXiv:1807.06579] [INSPIRE].Google Scholar
  88. [88]
    F. Denef, A. Hebecker and T. Wrase, De Sitter swampland conjecture and the Higgs potential, Phys. Rev. D 98 (2018) 086004 [arXiv:1807.06581] [INSPIRE].ADSGoogle Scholar
  89. [89]
    E. Ó. Colgáin, M.H. P.M. Van Putten and H. Yavartanoo, Observational consequences of H 0 tension in de Sitter swampland, arXiv:1807.07451 [INSPIRE].
  90. [90]
    C. Roupec and T. Wrase, De Sitter extrema and the swampland, Fortsch. Phys. 67 (2019) 1800082 [arXiv:1807.09538] [INSPIRE].Google Scholar
  91. [91]
    D. Andriot, New constraints on classical de Sitter: flirting with the swampland, Fortsch. Phys. 67 (2019) 1800103 [arXiv:1807.09698] [INSPIRE].Google Scholar
  92. [92]
    H. Matsui and F. Takahashi, Eternal inflation and swampland conjectures, Phys. Rev. D 99 (2019) 023533 [arXiv:1807.11938] [INSPIRE].ADSGoogle Scholar
  93. [93]
    I. Ben-Dayan, Draining the swampland, arXiv:1808.01615 [INSPIRE].
  94. [94]
    C. Damian and O. Loaiza-Brito, Two-field axion inflation and the swampland constraint in the flux-scaling scenario, Fortsch. Phys. 67 (2019) 1800072 [arXiv:1808.03397] [INSPIRE].Google Scholar
  95. [95]
    J.P. Conlon, The de Sitter swampland conjecture and supersymmetric AdS vacua, Int. J. Mod. Phys. A 33 (2018) 1850178 [arXiv:1808.05040] [INSPIRE].ADSGoogle Scholar
  96. [96]
    W.H. Kinney, S. Vagnozzi and L. Visinelli, The zoo plot meets the swampland: mutual (in)consistency of single-field inflation, string conjectures and cosmological data, arXiv:1808.06424 [INSPIRE].
  97. [97]
    K. Dasgupta, M. Emelin, E. McDonough and R. Tatar, Quantum corrections and the de Sitter swampland conjecture, JHEP 01 (2019) 145 [arXiv:1808.07498] [INSPIRE].ADSGoogle Scholar
  98. [98]
    H. Murayama, M. Yamazaki and T.T. Yanagida, Do we live in the swampland?, JHEP 12 (2018) 032 [arXiv:1809.00478] [INSPIRE].ADSGoogle Scholar
  99. [99]
    S. Brahma and M. Wali Hossain, Avoiding the string swampland in single-field inflation: excited initial states, JHEP 03 (2019) 006 [arXiv:1809.01277] [INSPIRE].Google Scholar
  100. [100]
    K. Choi, D. Chway and C.S. Shin, The dS swampland conjecture with the electroweak symmetry and QCD chiral symmetry breaking, JHEP 11 (2018) 142 [arXiv:1809.01475] [INSPIRE].ADSGoogle Scholar
  101. [101]
    S. Das, A note on single-field inflation and the swampland criteria, arXiv:1809.03962 [INSPIRE].
  102. [102]
    U. Danielsson, The quantum swampland, arXiv:1809.04512 [INSPIRE].
  103. [103]
    D. Wang, The multi-feature universe: large parameter space cosmology and the swampland, arXiv:1809.04854 [INSPIRE].
  104. [104]
    C. Han, S. Pi and M. Sasaki, Quintessence saves Higgs instability, arXiv:1809.05507 [INSPIRE].
  105. [105]
    J. Moritz, A. Retolaza and A. Westphal, On uplifts by warped anti-D3-branes, Fortsch. Phys. 67 (2019) 1800098 [arXiv:1809.06618] [INSPIRE].Google Scholar
  106. [106]
    I. Bena, E. Dudas, M. Graña and S. Lüst, Uplifting runaways, Fortsch. Phys. 67 (2019) 1800100 [arXiv:1809.06861] [INSPIRE].Google Scholar
  107. [107]
    K. Dimopoulos, Steep eternal inflation and the swampland, Phys. Rev. D 98 (2018) 123516 [arXiv:1810.03438] [INSPIRE].ADSGoogle Scholar
  108. [108]
    L. Heisenberg, M. Bartelmann, R. Brandenberger and A. Refregier, Dark energy in the swampland II, arXiv:1809.00154 [INSPIRE].
  109. [109]
    L. Heisenberg, M. Bartelmann, R. Brandenberger and A. Refregier, Dark energy in the swampland, Phys. Rev. D 98 (2018) 123502 [arXiv:1808.02877] [INSPIRE].ADSGoogle Scholar
  110. [110]
    G. D’Amico, N. Kaloper and A. Lawrence, Strongly coupled quintessence, arXiv:1809.05109 [INSPIRE].
  111. [111]
    A. Ashoorioon, Rescuing single field inflation from the swampland, Phys. Lett. B 790 (2019) 568 [arXiv:1810.04001] [INSPIRE].Google Scholar
  112. [112]
    S.D. Odintsov and V.K. Oikonomou, Finite-time singularities in swampland-related dark energy models, arXiv:1810.03575 [INSPIRE].
  113. [113]
    M. Motaharfar, V. Kamali and R.O. Ramos, Warm way out of the swampland, arXiv:1810.02816 [INSPIRE].
  114. [114]
    M. Kawasaki and V. Takhistov, Primordial black holes and the string swampland, Phys. Rev. D 98 (2018) 123514 [arXiv:1810.02547] [INSPIRE].ADSGoogle Scholar
  115. [115]
    K. Hamaguchi, M. Ibe and T. Moroi, The swampland conjecture and the Higgs expectation value, JHEP 12 (2018) 023 [arXiv:1810.02095] [INSPIRE].ADSGoogle Scholar
  116. [116]
    C.-M. Lin, K.-W. Ng and K. Cheung, Chaotic inflation on the brane and the swampland criteria, arXiv:1810.01644 [INSPIRE].
  117. [117]
    J. Ellis, B. Nagaraj, D.V. Nanopoulos and K.A. Olive, De Sitter vacua in no-scale supergravity, JHEP 11 (2018) 110 [arXiv:1809.10114] [INSPIRE].ADSzbMATHGoogle Scholar
  118. [118]
    S. Das, Warm inflation in the light of swampland criteria, arXiv:1810.05038 [INSPIRE].
  119. [119]
    H. Ooguri, E. Palti, G. Shiu and C. Vafa, Distance and de Sitter conjectures on the swampland, Phys. Lett. B 788 (2019) 180 [arXiv:1810.05506] [INSPIRE].ADSMathSciNetGoogle Scholar
  120. [120]
    S.-J. Wang, Electroweak relaxation of cosmological hierarchy, Phys. Rev. D 99 (2019) 023529 [arXiv:1810.06445] [INSPIRE].ADSGoogle Scholar
  121. [121]
    H. Fukuda, R. Saito, S. Shirai and M. Yamazaki, Phenomenological consequences of the refined swampland conjecture, arXiv:1810.06532 [INSPIRE].
  122. [122]
    A. Hebecker and T. Wrase, The asymptotic dS swampland conjecture — A simplified derivation and a potential loophole, Fortsch. Phys. 67 (2019) 1800097 [arXiv:1810.08182] [INSPIRE].Google Scholar
  123. [123]
    F.F. Gautason, V. Van Hemelryck and T. Van Riet, The tension between 10D supergravity and dS uplifts, Fortsch. Phys. 67 (2019) 1800091 [arXiv:1810.08518] [INSPIRE].Google Scholar
  124. [124]
    S.K. Garg, C. Krishnan and M. Zaid, Bounds on slow roll at the boundary of the landscape, arXiv:1810.09406 [INSPIRE].
  125. [125]
    S.C. Park, Minimal gauge inflation and the refined swampland conjecture, JCAP 01 (2019) 053 [arXiv:1810.11279] [INSPIRE].ADSGoogle Scholar
  126. [126]
    J. Blåbäck, U. Danielsson and G. Dibitetto, A new light on the darkest corner of the landscape, arXiv:1810.11365 [INSPIRE].
  127. [127]
    R. Schimmrigk, The swampland spectrum conjecture in inflation, arXiv:1810.11699 [INSPIRE].
  128. [128]
    C.-M. Lin, Type I hilltop inflation and the refined swampland criteria, Phys. Rev. D 99 (2019) 023519 [arXiv:1810.11992] [INSPIRE].ADSGoogle Scholar
  129. [129]
    P. Agrawal and G. Obied, Dark energy and the refined de Sitter conjecture, arXiv:1811.00554 [INSPIRE].
  130. [130]
    Z. Yi and Y. Gong, Gauss-Bonnet inflation and swampland, arXiv:1811.01625 [INSPIRE].
  131. [131]
    J.J. Heckman, C. Lawrie, L. Lin and G. Zoccarato, F-theory and dark energy, arXiv:1811.01959 [INSPIRE].
  132. [132]
    C.-I. Chiang, J.M. Leedom and H. Murayama, What does inflation say about dark energy given the swampland conjectures?, arXiv:1811.01987 [INSPIRE].
  133. [133]
    D.Y. Cheong, S.M. Lee and S.C. Park, Higgs inflation and the refined dS conjecture, Phys. Lett. B 789 (2019) 336 [arXiv:1811.03622] [INSPIRE].ADSGoogle Scholar
  134. [134]
    E. Elizalde and M. Khurshudyan, Swampland criteria for a dark-energy dominated universe, ensuing from Gaussian process and H(z) data analysis, arXiv:1811.03861 [INSPIRE].
  135. [135]
    J.J. Blanco-Pillado, M.A. Urkiola and J.M. Wachter, Racetrack potentials and the de Sitter swampland conjectures, JHEP 01 (2019) 187 [arXiv:1811.05463] [INSPIRE].ADSGoogle Scholar
  136. [136]
    M. Ibe, M. Yamazaki and T.T. Yanagida, Quintessence axion from swampland conjectures, arXiv:1811.04664 [INSPIRE].
  137. [137]
    R. Holman and B. Richard, A spinodal solution to swampland inflationary constraints, arXiv:1811.06021 [INSPIRE].
  138. [138]
    D. Junghans, Weakly coupled de Sitter vacua with fluxes and the swampland, arXiv:1811.06990 [INSPIRE].
  139. [139]
    A. Banlaki, A. Chowdhury, C. Roupec and T. Wrase, Scaling limits of dS vacua and the swampland, arXiv:1811.07880 [INSPIRE].
  140. [140]
    D. Andriot and C. Roupec, Further refining the de Sitter swampland conjecture, Fortsch. Phys. 67 (2019) 1800105 [arXiv:1811.08889] [INSPIRE].Google Scholar
  141. [141]
    Y. Wang, L. Pogosian, G.B. Zhao and A. Zucca, Evolution of dark energy reconstructed from the latest observations, Astrophys. J. 869 (2018) L8 [arXiv:1807.03772] [INSPIRE].ADSGoogle Scholar
  142. [142]
    S. Capozziello, Ruchika and A.A. Sen, Model independent constraints on dark energy evolution from low-redshift observations, Mon. Not. Roy. Astron. Soc. 484 (2019) 4484 [arXiv:1806.03943] [INSPIRE].
  143. [143]
    K. Dutta et al., Negative cosmological constant is consistent with cosmological data, arXiv:1808.06623 [INSPIRE].
  144. [144]
    J.G. Russo and P.K. Townsend, Late-time cosmic acceleration from compactification, arXiv:1811.03660 [INSPIRE].
  145. [145]
    J.P. Conlon and F. Quevedo, Putting the boot into the swampland, arXiv:1811.06276 [INSPIRE].
  146. [146]
    S. Tsujikawa, Quintessence: a review, Class. Quant. Grav. 30 (2013) 214003 [arXiv:1304.1961] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  147. [147]
    S.M. Carroll, Quintessence and the rest of the world, Phys. Rev. Lett. 81 (1998) 3067 [astro-ph/9806099] [INSPIRE].
  148. [148]
    C.J. A.P. Martins, The status of varying constants: a review of the physics, searches and implications, arXiv:1709.02923 [INSPIRE].
  149. [149]
    T. Banks, M. Dine and M.R. Douglas, Time varying alpha and particle physics, Phys. Rev. Lett. 88 (2002) 131301 [hep-ph/0112059] [INSPIRE].
  150. [150]
    M. Garny, Quantum corrections in quintessence models, Phys. Rev. D 74 (2006) 043009 [hep-ph/0606120] [INSPIRE].
  151. [151]
    M.C. David Marsh, The swampland, quintessence and the vacuum energy, Phys. Lett. B 789 (2019) 639 [arXiv:1809.00726] [INSPIRE].ADSGoogle Scholar
  152. [152]
    M.A. Luty and R. Sundrum, Hierarchy stabilization in warped supersymmetry, Phys. Rev. D 64 (2001) 065012 [hep-th/0012158] [INSPIRE].ADSMathSciNetGoogle Scholar
  153. [153]
    A. Anisimov, M. Dine, M. Graesser and S.D. Thomas, Brane world SUSY breaking, Phys. Rev. D 65 (2002) 105011 [hep-th/0111235] [INSPIRE].ADSGoogle Scholar
  154. [154]
    S. Kachru, J. McGreevy and P. Svrček, Bounds on masses of bulk fields in string compactifications, JHEP 04 (2006) 023 [hep-th/0601111] [INSPIRE].ADSMathSciNetGoogle Scholar
  155. [155]
    S. Kachru, L. McAllister and R. Sundrum, Sequestering in string theory, JHEP 10 (2007) 013 [hep-th/0703105] [INSPIRE].ADSMathSciNetGoogle Scholar
  156. [156]
    E. Palti, The weak gravity conjecture and scalar fields, JHEP 08 (2017) 034 [arXiv:1705.04328] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  157. [157]
    J.P. Conlon and F. Quevedo, Astrophysical and cosmological implications of large volume string compactifications, JCAP 08 (2007) 019 [arXiv:0705.3460] [INSPIRE].ADSMathSciNetGoogle Scholar
  158. [158]
    M. Cicoli and A. Mazumdar, Reheating for closed string inflation, JCAP 09 (2010) 025 [arXiv:1005.5076] [INSPIRE].ADSGoogle Scholar
  159. [159]
    S. Schlamminger et al., Test of the equivalence principle using a rotating torsion balance, Phys. Rev. Lett. 100 (2008) 041101 [arXiv:0712.0607] [INSPIRE].ADSGoogle Scholar
  160. [160]
    J.G. Williams, S.G. Turyshev and D.H. Boggs, Progress in lunar laser ranging tests of relativistic gravity, Phys. Rev. Lett. 93 (2004) 261101 [gr-qc/0411113] [INSPIRE].
  161. [161]
    R. Blumenhagen, S. Moster and E. Plauschinn, Moduli stabilisation versus chirality for MSSM like type IIB orientifolds, JHEP 01 (2008) 058 [arXiv:0711.3389] [INSPIRE].ADSMathSciNetGoogle Scholar
  162. [162]
    J.P. Conlon, D. Cremades and F. Quevedo, Kähler potentials of chiral matter fields for Calabi-Yau string compactifications, JHEP 01 (2007) 022 [hep-th/0609180] [INSPIRE].ADSGoogle Scholar
  163. [163]
    L. Aparicio, D.G. Cerdeno and L.E. Ibáñez, Modulus-dominated SUSY-breaking soft terms in F-theory and their test at LHC, JHEP 07 (2008) 099 [arXiv:0805.2943] [INSPIRE].ADSMathSciNetGoogle Scholar
  164. [164]
    L. Aparicio, F. Quevedo and R. Valandro, Moduli stabilisation with nilpotent goldstino: vacuum structure and SUSY breaking, JHEP 03 (2016) 036 [arXiv:1511.08105] [INSPIRE].ADSGoogle Scholar
  165. [165]
    R. Blumenhagen et al., SUSY breaking in local string/F-theory models, JHEP 09 (2009) 007 [arXiv:0906.3297] [INSPIRE].ADSMathSciNetGoogle Scholar
  166. [166]
    J.P. Conlon and L.T. Witkowski, Scattering and sequestering of blow-up moduli in local string models, JHEP 12 (2011) 028 [arXiv:1109.4153] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  167. [167]
    C.P. Burgess et al., Non-standard primordial fluctuations and non-Gaussianity in string inflation, JHEP 08 (2010) 045 [arXiv:1005.4840] [INSPIRE].ADSzbMATHGoogle Scholar
  168. [168]
    K. Becker, M. Becker, M. Haack and J. Louis, Supersymmetry breaking and αcorrections to flux induced potentials, JHEP 06 (2002) 060 [hep-th/0204254] [INSPIRE].ADSMathSciNetGoogle Scholar
  169. [169]
    J.P. Conlon, A. Maharana and F. Quevedo, Towards realistic string vacua, JHEP 05 (2009) 109 [arXiv:0810.5660] [INSPIRE].ADSGoogle Scholar
  170. [170]
    M. Berg, M. Haack and B. Körs, String loop corrections to Kähler potentials in orientifolds, JHEP 11 (2005) 030 [hep-th/0508043] [INSPIRE].ADSGoogle Scholar
  171. [171]
    J.P. Conlon, Moduli stabilisation and applications in IIB string theory, Fortsch. Phys. 55 (2007) 287 [hep-th/0611039] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  172. [172]
    M. Berg, M. Haack and E. Pajer, Jumping through loops: on soft terms from large volume compactifications, JHEP 09 (2007) 031 [arXiv:0704.0737] [INSPIRE].ADSMathSciNetGoogle Scholar
  173. [173]
    M. Cicoli, J.P. Conlon and F. Quevedo, Systematics of string loop corrections in type IIB calabi-yau flux compactifications, JHEP 01 (2008) 052 [arXiv:0708.1873] [INSPIRE].ADSMathSciNetGoogle Scholar
  174. [174]
    M. Cicoli, J.P. Conlon and F. Quevedo, General analysis of LARGE volume scenarios with string loop moduli stabilisation, JHEP 10 (2008) 105 [arXiv:0805.1029] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  175. [175]
    Y. Aghababaie, C.P. Burgess, S.L. Parameswaran and F. Quevedo, Towards a naturally small cosmological constant from branes in 6D supergravity, Nucl. Phys. B 680 (2004) 389 [hep-th/0304256] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  176. [176]
    M. Cicoli, C.P. Burgess and F. Quevedo, Anisotropic modulus stabilisation: strings at LHC scales with micron-sized extra dimensions, JHEP 10 (2011) 119 [arXiv:1105.2107] [INSPIRE].ADSzbMATHGoogle Scholar
  177. [177]
    M. Cicoli, M. Kreuzer and C. Mayrhofer, Toric K3-fibred Calabi-Yau manifolds with del Pezzo divisors for string compactifications, JHEP 02 (2012) 002 [arXiv:1107.0383] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  178. [178]
    C.P. Burgess, M. Cicoli, S. de Alwis and F. Quevedo, Robust inflation from fibrous strings, JCAP 05 (2016) 032 [arXiv:1603.06789] [INSPIRE].ADSMathSciNetGoogle Scholar
  179. [179]
    B. Holdom, Two U(1)’s and epsilon charge shifts, Phys. Lett. B 166 (1986) 196.ADSGoogle Scholar
  180. [180]
    K.R. Dienes, C.F. Kolda and J. March-Russell, Kinetic mixing and the supersymmetric gauge hierarchy, Nucl. Phys. B 492 (1997) 104 [hep-ph/9610479] [INSPIRE].
  181. [181]
    S.A. Abel et al., Kinetic mixing of the photon with hidden U(1)s in string phenomenology, JHEP 07 (2008) 124 [arXiv:0803.1449] [INSPIRE].ADSMathSciNetGoogle Scholar
  182. [182]
    C.P. Burgess et al., Continuous global symmetries and hyperweak interactions in string compactifications, JHEP 07 (2008) 073 [arXiv:0805.4037] [INSPIRE].ADSMathSciNetGoogle Scholar
  183. [183]
    S.A. Abel, J. Jaeckel, V.V. Khoze and A. Ringwald, Illuminating the hidden sector of string theory by shining light through a magnetic field, Phys. Lett. B 666 (2008) 66 [hep-ph/0608248] [INSPIRE].
  184. [184]
    M. Goodsell and A. Ringwald, Light hidden-sector U(1)s in string compactifications, Fortsch. Phys. 58 (2010) 716 [arXiv:1002.1840] [INSPIRE].ADSGoogle Scholar
  185. [185]
    M. Bullimore, J.P. Conlon and L.T. Witkowski, Kinetic mixing of U(1)s for local string models, JHEP 11 (2010) 142 [arXiv:1009.2380] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  186. [186]
    M. Cicoli, M. Goodsell, J. Jaeckel and A. Ringwald, Testing string vacua in the lab: from a hidden CMB to dark forces in flux compactifications, JHEP 07 (2011) 114 [arXiv:1103.3705] [INSPIRE].ADSzbMATHGoogle Scholar
  187. [187]
    M. Goodsell, S. Ramos-Sanchez and A. Ringwald, Kinetic mixing of U(1)s in heterotic orbifolds, JHEP 01 (2012) 021 [arXiv:1110.6901] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  188. [188]
    T. Damour and A.M. Polyakov, String theory and gravity, Gen. Rel. Grav. 26 (1994) 1171 [gr-qc/9411069] [INSPIRE].
  189. [189]
    T. Damour, F. Piazza and G. Veneziano, Runaway dilaton and equivalence principle violations, Phys. Rev. Lett. 89 (2002) 081601 [gr-qc/0204094] [INSPIRE].
  190. [190]
    P. Brax, C. van de Bruck, J. Martin and A.-C. Davis, Decoupling dark energy from matter, JCAP 09 (2009) 032 [arXiv:0904.3471] [INSPIRE].ADSGoogle Scholar
  191. [191]
    A. Maharana, Symmetry breaking bulk effects in local D-brane models, JHEP 06 (2012) 002 [arXiv:1111.3047] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  192. [192]
    T. Kobayashi, S.L. Parameswaran, S. Ramos-Sanchez and I. Zavala, Revisiting coupling selection rules in heterotic orbifold models, JHEP 05 (2012) 008 [Erratum ibid. 12 (2012) 049] [arXiv:1107.2137] [INSPIRE].
  193. [193]
    M. Berg, D. Marsh, L. McAllister and E. Pajer, Sequestering in string compactifications, JHEP 06 (2011) 134 [arXiv:1012.1858] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  194. [194]
    M. Berg, J.P. Conlon, D. Marsh and L.T. Witkowski, Superpotential de-sequestering in string models, JHEP 02 (2013) 018 [arXiv:1207.1103] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  195. [195]
    M.D. Goodsell and L.T. Witkowski, Instanton induced Yukawa couplings from distant E 3 and E −1 instantons, JHEP 01 (2016) 027 [arXiv:1509.00852] [INSPIRE].ADSzbMATHGoogle Scholar
  196. [196]
    S.B. Giddings and A. Maharana, Dynamics of warped compactifications and the shape of the warped landscape, Phys. Rev. D 73 (2006) 126003 [hep-th/0507158] [INSPIRE].ADSMathSciNetGoogle Scholar
  197. [197]
    A.R. Frey and A. Maharana, Warped spectroscopy: localization of frozen bulk modes, JHEP 08 (2006) 021 [hep-th/0603233] [INSPIRE].ADSMathSciNetGoogle Scholar
  198. [198]
    J. Khoury, Theories of dark energy with screening mechanisms, arXiv:1011.5909 [INSPIRE].
  199. [199]
    A.I. Vainshtein, To the problem of nonvanishing gravitation mass, Phys. Lett. B 39 (1972) 393.ADSGoogle Scholar
  200. [200]
    P. Brax et al., Detecting dark energy in orbit — The cosmological chameleon, Phys. Rev. D 70 (2004) 123518 [astro-ph/0408415] [INSPIRE].
  201. [201]
    C. Armendariz-Picon, V.F. Mukhanov and P.J. Steinhardt, A Dynamical solution to the problem of a small cosmological constant and late time cosmic acceleration, Phys. Rev. Lett. 85 (2000) 4438 [astro-ph/0004134] [INSPIRE].
  202. [202]
    K. Hinterbichler and J. Khoury, Symmetron fields: screening long-range forces through local symmetry restoration, Phys. Rev. Lett. 104 (2010) 231301 [arXiv:1001.4525] [INSPIRE].ADSGoogle Scholar
  203. [203]
    J. Martin, Quintessence: a mini-review, Mod. Phys. Lett. A 23 (2008) 1252 [arXiv:0803.4076] [INSPIRE].ADSGoogle Scholar
  204. [204]
    P. Brax and J. Martin, Moduli fields as quintessence and the chameleon, Phys. Lett. B 647 (2007) 320 [hep-th/0612208] [INSPIRE].ADSGoogle Scholar
  205. [205]
    P. Brax and J. Martin, Quintessence and supergravity, Phys. Lett. B 468 (1999) 40 [astro-ph/9905040] [INSPIRE].
  206. [206]
    E.J. Copeland, N.J. Nunes and F. Rosati, Quintessence models in supergravity, Phys. Rev. D 62 (2000) 123503 [hep-ph/0005222] [INSPIRE].
  207. [207]
    C.-I. Chiang and H. Murayama, Building supergravity quintessence model, arXiv:1808.02279 [INSPIRE].
  208. [208]
    R. Kallosh, A.D. Linde, S. Prokushkin and M. Shmakova, Supergravity, dark energy and the fate of the universe, Phys. Rev. D 66 (2002) 123503 [hep-th/0208156] [INSPIRE].ADSMathSciNetGoogle Scholar
  209. [209]
    D.B. Kaplan and M.B. Wise, Couplings of a light dilaton and violations of the equivalence principle, JHEP 08 (2000) 037 [hep-ph/0008116] [INSPIRE].
  210. [210]
    C.P. Burgess, A. Maharana and F. Quevedo, Uber-naturalness: unexpectedly light scalars from supersymmetric extra dimensions, JHEP 05 (2011) 010 [arXiv:1005.1199] [INSPIRE].ADSzbMATHGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Bobby Samir Acharya
    • 1
    • 2
  • Anshuman Maharana
    • 3
  • Francesco Muia
    • 2
    Email author
  1. 1.Theoretical Particle Physics & Cosmology Group, Department of PhysicsKing’s College LondonLondonUnited Kingdom
  2. 2.ICTPTriesteItaly
  3. 3.Harish Chandra Research Institute, Homi Bhabha National InstituteAllahabadIndia

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