Advertisement

Generalized gravity from modified DFT

  • Yuho SakataniEmail author
  • Shozo Uehara
  • Kentaroh Yoshida
Open Access
Regular Article - Theoretical Physics

Abstract

Recently, generalized equations of type IIB supergravity have been derived from the requirement of classical kappa-symmetry of type IIB superstring theory in the Green-Schwarz formulation. These equations are covariant under generalized T -duality transformations and hence one may expect a formulation similar to double field theory (DFT). In this paper, we consider a modification of the DFT equations of motion by relaxing a condition for the generalized covariant derivative with an extra generalized vector. In this modified double field theory (mDFT), we show that the flatness condition of the modified generalized Ricci tensor leads to the NS-NS part of the generalized equations of type IIB supergravity. In particular, the extra vector fields appearing in the generalized equations correspond to the extra generalized vector in mDFT. We also discuss duality symmetries and a modification of the string charge in mDFT.

Keywords

String Duality Supergravity Models Integrable Field Theories 

Notes

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.

References

  1. [1]
    L. Wulff and A.A. Tseytlin, κ-symmetry of superstring σ-model and generalized 10d supergravity equations, JHEP 06 (2016) 174 [arXiv:1605.04884] [INSPIRE].
  2. [2]
    G. Arutyunov, S. Frolov, B. Hoare, R. Roiban and A.A. Tseytlin, Scale invariance of the η-deformed AdS 5 × S 5 superstring, T-duality and modified type-II equations, Nucl. Phys. B 903 (2016) 262 [arXiv:1511.05795] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  3. [3]
    M.T. Grisaru, P.S. Howe, L. Mezincescu, B. Nilsson and P.K. Townsend, N = 2 Superstrings in a Supergravity Background, Phys. Lett. B 162 (1985) 116 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  4. [4]
    E. Bergshoeff, E. Sezgin and P.K. Townsend, Superstring Actions in D = 3, 4, 6, 10 Curved Superspace, Phys. Lett. B 169 (1986) 191 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    C. Klimčík, Yang-Baxter σ-models and dS/AdS T duality, JHEP 12 (2002) 051 [hep-th/0210095] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    C. Klimčík, On integrability of the Yang-Baxter σ-model, J. Math. Phys. 50 (2009) 043508 [arXiv:0802.3518] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  7. [7]
    C. Klimčík, Integrability of the bi-Yang-Baxter σ-model, Lett. Math. Phys. 104 (2014) 1095 [arXiv:1402.2105] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  8. [8]
    F. Delduc, M. Magro and B. Vicedo, On classical q-deformations of integrable σ-models, JHEP 11 (2013) 192 [arXiv:1308.3581] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  9. [9]
    T. Matsumoto and K. Yoshida, Yang-Baxter σ-models based on the CYBE, Nucl. Phys. B 893 (2015) 287 [arXiv:1501.03665] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  10. [10]
    F. Delduc, M. Magro and B. Vicedo, An integrable deformation of the AdS 5×S 5 superstring action, Phys. Rev. Lett. 112 (2014) 051601 [arXiv:1309.5850] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    F. Delduc, M. Magro and B. Vicedo, Derivation of the action and symmetries of the q-deformed AdS 5 × S 5 superstring, JHEP 10 (2014) 132 [arXiv:1406.6286] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  12. [12]
    I. Kawaguchi, T. Matsumoto and K. Yoshida, Jordanian deformations of the AdS 5 xS 5 superstring, JHEP 04 (2014) 153 [arXiv:1401.4855] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    V.G. Drinfeld, Hopf algebras and the quantum Yang-Baxter equation, Sov. Math. Dokl. 32 (1985) 254 [INSPIRE].Google Scholar
  14. [14]
    V.G. Drinfeld, Quantum groups, J. Sov. Math. 41 (1988) 898 [INSPIRE].CrossRefGoogle Scholar
  15. [15]
    M. Jimbo, A q difference analog of U(g) and the Yang-Baxter equation, Lett. Math. Phys. 10 (1985) 63 [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  16. [16]
    G. Arutyunov, R. Borsato and S. Frolov, S-matrix for strings on η-deformed AdS5 x S5, JHEP 04 (2014) 002 [arXiv:1312.3542] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    G. Arutyunov, R. Borsato and S. Frolov, Puzzles of η-deformed AdS 5× S 5, JHEP 12 (2015) 049 [arXiv:1507.04239] [INSPIRE].ADSGoogle Scholar
  18. [18]
    B. Hoare and A.A. Tseytlin, Type IIB supergravity solution for the T-dual of the η-deformed AdS 5× S 5 superstring, JHEP 10 (2015) 060 [arXiv:1508.01150] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    B. Hoare and A.A. Tseytlin, On integrable deformations of superstring σ-models related to AdS n × S n supercosets, Nucl. Phys. B 897 (2015) 448 [arXiv:1504.07213] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  20. [20]
    T. Matsumoto and K. Yoshida, Lunin-Maldacena backgrounds from the classical Yang-Baxter equationtowards the gravity/CYBE correspondence, JHEP 06 (2014) 135 [arXiv:1404.1838] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  21. [21]
    T. Matsumoto and K. Yoshida, Integrability of classical strings dual for noncommutative gauge theories, JHEP 06 (2014) 163 [arXiv:1404.3657] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  22. [22]
    T. Matsumoto and K. Yoshida, Schrödinger geometries arising from Yang-Baxter deformations, JHEP 04 (2015) 180 [arXiv:1502.00740] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    I. Kawaguchi, T. Matsumoto and K. Yoshida, A Jordanian deformation of AdS space in type IIB supergravity, JHEP 06 (2014) 146 [arXiv:1402.6147] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  24. [24]
    T. Matsumoto and K. Yoshida, Yang-Baxter deformations and string dualities, JHEP 03 (2015) 137 [arXiv:1412.3658] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  25. [25]
    T. Matsumoto and K. Yoshida, Integrable deformations of the AdS 5 × S 5 superstring and the classical Yang-Baxter equation — Towards the gravity/CYBE correspondence —, J. Phys. Conf. Ser. 563 (2014) 012020 [arXiv:1410.0575] [INSPIRE].CrossRefGoogle Scholar
  26. [26]
    T. Matsumoto and K. Yoshida, Towards the gravity/CYBE correspondence — the current status —, J. Phys. Conf. Ser. 670 (2016) 012033 [INSPIRE].CrossRefGoogle Scholar
  27. [27]
    S.J. van Tongeren, On classical Yang-Baxter based deformations of the AdS 5 × S5 superstring, JHEP 06 (2015) 048 [arXiv:1504.05516] [INSPIRE].CrossRefGoogle Scholar
  28. [28]
    S.J. van Tongeren, Yang-Baxter deformations, AdS/CFT and twist-noncommutative gauge theory, Nucl. Phys. B 904 (2016) 148 [arXiv:1506.01023] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  29. [29]
    P.M. Crichigno, T. Matsumoto and K. Yoshida, Deformations of T 1,1 as Yang-Baxter σ-models, JHEP 12 (2014) 085 [arXiv:1406.2249] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    P. Marcos Crichigno, T. Matsumoto and K. Yoshida, Towards the gravity/CYBE correspondence beyond integrabilityYang-Baxter deformations of T 1,1, J. Phys. Conf. Ser. 670 (2016) 012019 [arXiv:1510.00835] [INSPIRE].CrossRefGoogle Scholar
  31. [31]
    H. Kyono and K. Yoshida, Supercoset construction of Yang-Baxter deformed AdS 5×S 5 backgrounds, PTEP 2016 (2016) 083B03 [arXiv:1605.02519] [INSPIRE].
  32. [32]
    B. Hoare and S.J. van Tongeren, On Jordanian deformations of AdS 5 and supergravity, J. Phys. A 49 (2016) 434006 [arXiv:1605.03554] [INSPIRE].zbMATHGoogle Scholar
  33. [33]
    D. Orlando, S. Reffert, J.-i. Sakamoto and K. Yoshida, Generalized type IIB supergravity equations and non-Abelian classical r-matrices, J. Phys. A 49 (2016) 445403 [arXiv:1607.00795] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  34. [34]
    R. Borsato and L. Wulff, Target space supergeometry of η and λ-deformed strings, JHEP 10 (2016) 045 [arXiv:1608.03570] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  35. [35]
    D. Osten and S.J. van Tongeren, Abelian Yang-Baxter deformations and TsT transformations, Nucl. Phys. B 915 (2017) 184 [arXiv:1608.08504] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  36. [36]
    S.J. van Tongeren, Almost abelian twists and AdS/CFT, Phys. Lett. B 765 (2017) 344 [arXiv:1610.05677] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  37. [37]
    W. Siegel, Two vierbein formalism for string inspired axionic gravity, Phys. Rev. D 47 (1993) 5453 [hep-th/9302036] [INSPIRE].ADSMathSciNetGoogle Scholar
  38. [38]
    W. Siegel, Superspace duality in low-energy superstrings, Phys. Rev. D 48 (1993) 2826 [hep-th/9305073] [INSPIRE].ADSMathSciNetGoogle Scholar
  39. [39]
    W. Siegel, Manifest duality in low-energy superstrings, hep-th/9308133 [INSPIRE].
  40. [40]
    C. Hull and B. Zwiebach, Double Field Theory, JHEP 09 (2009) 099 [arXiv:0904.4664] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  41. [41]
    C. Hull and B. Zwiebach, The Gauge algebra of double field theory and Courant brackets, JHEP 09 (2009) 090 [arXiv:0908.1792] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  42. [42]
    O. Hohm, C. Hull and B. Zwiebach, Background independent action for double field theory, JHEP 07 (2010) 016 [arXiv:1003.5027] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  43. [43]
    O. Hohm, C. Hull and B. Zwiebach, Generalized metric formulation of double field theory, JHEP 08 (2010) 008 [arXiv:1006.4823] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  44. [44]
    I. Jeon, K. Lee and J.-H. Park, Differential geometry with a projection: Application to double field theory, JHEP 04 (2011) 014 [arXiv:1011.1324] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  45. [45]
    O. Hohm and S.K. Kwak, Frame-like Geometry of Double Field Theory, J. Phys. A 44 (2011) 085404 [arXiv:1011.4101] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  46. [46]
    I. Jeon, K. Lee and J.-H. Park, Stringy differential geometry, beyond Riemann, Phys. Rev. D 84 (2011) 044022 [arXiv:1105.6294] [INSPIRE].ADSGoogle Scholar
  47. [47]
    O. Hohm, S.K. Kwak and B. Zwiebach, Unification of Type II Strings and T-duality, Phys. Rev. Lett. 107 (2011) 171603 [arXiv:1106.5452] [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    O. Hohm, S.K. Kwak and B. Zwiebach, Double Field Theory of Type II Strings, JHEP 09 (2011) 013 [arXiv:1107.0008] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  49. [49]
    I. Jeon, K. Lee and J.-H. Park, Incorporation of fermions into double field theory, JHEP 11 (2011) 025 [arXiv:1109.2035] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  50. [50]
    O. Hohm and B. Zwiebach, On the Riemann Tensor in Double Field Theory, JHEP 05 (2012) 126 [arXiv:1112.5296] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  51. [51]
    O. Hohm and S.K. Kwak, N = 1 Supersymmetric Double Field Theory, JHEP 03 (2012) 080 [arXiv:1111.7293] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  52. [52]
    I. Jeon, K. Lee and J.-H. Park, Supersymmetric Double Field Theory: Stringy Reformulation of Supergravity, Phys. Rev. D 85 (2012) 081501 [Erratum ibid. D 86 (2012) 089903] [arXiv:1112.0069] [INSPIRE].
  53. [53]
    I. Jeon, K. Lee and J.-H. Park, Ramond-Ramond Cohomology and O(D,D) T-duality, JHEP 09 (2012) 079 [arXiv:1206.3478] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  54. [54]
    I. Jeon, K. Lee, J.-H. Park and Y. Suh, Stringy Unification of Type IIA and IIB Supergravities under N = 2 D = 10 Supersymmetric Double Field Theory, Phys. Lett. B 723 (2013) 245 [arXiv:1210.5078] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  55. [55]
    B. Zwiebach, Double Field Theory, T-duality and Courant Brackets, Lect. Notes Phys. 851 (2012) 265 [arXiv:1109.1782] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  56. [56]
    G. Aldazabal, D. Marques and C. Núñez, Double Field Theory: A Pedagogical Review, Class. Quant. Grav. 30 (2013) 163001 [arXiv:1305.1907] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  57. [57]
    D.S. Berman and D.C. Thompson, Duality Symmetric String and M-theory, Phys. Rept. 566 (2014) 1 [arXiv:1306.2643] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  58. [58]
    O. Hohm, D. Lüst and B. Zwiebach, The Spacetime of Double Field Theory: Review, Remarks and Outlook, Fortsch. Phys. 61 (2013) 926 [arXiv:1309.2977] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  59. [59]
    A. Baguet, M. Magro and H. Samtleben, Generalized IIB supergravity from exceptional field theory, JHEP 03 (2017) 100 [arXiv:1612.07210] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  60. [60]
    C.M. Hull and P.K. Townsend, Finiteness and Conformal Invariance in Nonlinear σ Models, Nucl. Phys. B 274 (1986) 349 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  61. [61]
    A.A. Tseytlin, Conformal Anomaly in Two-Dimensional σ-model on Curved Background and Strings, Phys. Lett. B 178 (1986) 34 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  62. [62]
    G.M. Shore, A Local Renormalization Group Equation, Diffeomorphisms and Conformal Invariance in σ Models, Nucl. Phys. B 286 (1987) 349 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  63. [63]
    A.A. Tseytlin, σ Model Weyl Invariance Conditions and String Equations of Motion, Nucl. Phys. B 294 (1987) 383 [INSPIRE].
  64. [64]
    K. Lee, Towards Weakly Constrained Double Field Theory, Nucl. Phys. B 909 (2016) 429 [arXiv:1509.06973] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  65. [65]
    C.-T. Ma and F. Pezzella, Supergravity with Doubled Spacetime Structure, Phys. Rev. D 95 (2017) 066016 [arXiv:1611.03690] [INSPIRE].ADSGoogle Scholar
  66. [66]
    J.-H. Park, S.-J. Rey, W. Rim and Y. Sakatani, O(D, D) covariant Noether currents and global charges in double field theory, JHEP 11 (2015) 131 [arXiv:1507.07545] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  67. [67]
    S.K. Kwak, Invariances and Equations of Motion in Double Field Theory, JHEP 10 (2010) 047 [arXiv:1008.2746] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  68. [68]
    C.G. Callan Jr., E.J. Martinec, M.J. Perry and D. Friedan, Strings in Background Fields, Nucl. Phys. B 262 (1985) 593 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  69. [69]
    A.A. Tseytlin, Duality Symmetric Formulation of String World Sheet Dynamics, Phys. Lett. B 242 (1990) 163 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  70. [70]
    A.A. Tseytlin, Duality symmetric closed string theory and interacting chiral scalars, Nucl. Phys. B 350 (1991) 395 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  71. [71]
    D.S. Berman, N.B. Copland and D.C. Thompson, Background Field Equations for the Duality Symmetric String, Nucl. Phys. B 791 (2008) 175 [arXiv:0708.2267] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  72. [72]
    D.S. Berman and D.C. Thompson, Duality Symmetric Strings, Dilatons and O(d,d) Effective Actions, Phys. Lett. B 662 (2008) 279 [arXiv:0712.1121] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  73. [73]
    N.B. Copland, Connecting T-duality invariant theories, Nucl. Phys. B 854 (2012) 575 [arXiv:1106.1888] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  74. [74]
    N.B. Copland, A Double σ-model for Double Field Theory, JHEP 04 (2012) 044 [arXiv:1111.1828] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  75. [75]
    C.D.A. Blair, Conserved Currents of Double Field Theory, JHEP 04 (2016) 180 [arXiv:1507.07541] [INSPIRE].ADSMathSciNetGoogle Scholar
  76. [76]
    R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) R3427 [gr-qc/9307038] [INSPIRE].
  77. [77]
    V. Iyer and R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50 (1994) 846 [gr-qc/9403028] [INSPIRE].
  78. [78]
    V. Iyer and R.M. Wald, A Comparison of Noether charge and Euclidean methods for computing the entropy of stationary black holes, Phys. Rev. D 52 (1995) 4430 [gr-qc/9503052] [INSPIRE].
  79. [79]
    A.S. Arvanitakis and C.D.A. Blair, Black hole thermodynamics, stringy dualities and double field theory, Class. Quant. Grav. 34 (2017) 055001 [arXiv:1608.04734] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  80. [80]
    P.C. West, E 11 and M-theory, Class. Quant. Grav. 18 (2001) 4443 [hep-th/0104081] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  81. [81]
    P.C. West, E 11 , SL(32) and central charges, Phys. Lett. B 575 (2003) 333 [hep-th/0307098] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  82. [82]
    P.C. West, The IIA, IIB and eleven-dimensional theories and their common E 11 origin, Nucl. Phys. B 693 (2004) 76 [hep-th/0402140] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  83. [83]
    C.M. Hull, Generalised Geometry for M-theory, JHEP 07 (2007) 079 [hep-th/0701203] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  84. [84]
    P. Pires Pacheco and D. Waldram, M-theory, exceptional generalised geometry and superpotentials, JHEP 09 (2008) 123 [arXiv:0804.1362] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  85. [85]
    C. Hillmann, Generalized E(7(7)) coset dynamics and D = 11 supergravity, JHEP 03 (2009) 135 [arXiv:0901.1581] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  86. [86]
    D.S. Berman and M.J. Perry, Generalized Geometry and M-theory, JHEP 06 (2011) 074 [arXiv:1008.1763] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  87. [87]
    D.S. Berman, H. Godazgar and M.J. Perry, SO(5,5) duality in M-theory and generalized geometry, Phys. Lett. B 700 (2011) 65 [arXiv:1103.5733] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  88. [88]
    D.S. Berman, H. Godazgar, M. Godazgar and M.J. Perry, The Local symmetries of M-theory and their formulation in generalised geometry, JHEP 01 (2012) 012 [arXiv:1110.3930] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  89. [89]
    D.S. Berman, H. Godazgar, M.J. Perry and P. West, Duality Invariant Actions and Generalised Geometry, JHEP 02 (2012) 108 [arXiv:1111.0459] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  90. [90]
    D.S. Berman, M. Cederwall, A. Kleinschmidt and D.C. Thompson, The gauge structure of generalised diffeomorphisms, JHEP 01 (2013) 064 [arXiv:1208.5884] [INSPIRE].ADSCrossRefGoogle Scholar
  91. [91]
    J.-H. Park and Y. Suh, U-geometry: SL(5), JHEP 04 (2013) 147 [Erratum ibid. 1311 (2013) 210] [arXiv:1302.1652] [INSPIRE].
  92. [92]
    G. Aldazabal, M. Graña, D. Marqués and J.A. Rosabal, Extended geometry and gauged maximal supergravity, JHEP 06 (2013) 046 [arXiv:1302.5419] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  93. [93]
    O. Hohm and H. Samtleben, Exceptional Form of D = 11 Supergravity, Phys. Rev. Lett. 111 (2013) 231601 [arXiv:1308.1673] [INSPIRE].ADSCrossRefGoogle Scholar
  94. [94]
    O. Hohm and H. Samtleben, Exceptional Field Theory I: E 6(6) covariant Form of M-theory and Type IIB, Phys. Rev. D 89 (2014) 066016 [arXiv:1312.0614] [INSPIRE].ADSGoogle Scholar
  95. [95]
    O. Hohm and H. Samtleben, Exceptional field theory. II. E 7(7), Phys. Rev. D 89 (2014) 066017 [arXiv:1312.4542] [INSPIRE].
  96. [96]
    H. Godazgar, M. Godazgar, O. Hohm, H. Nicolai and H. Samtleben, Supersymmetric E 7(7) Exceptional Field Theory, JHEP 09 (2014) 044 [arXiv:1406.3235] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  97. [97]
    O. Hohm and H. Samtleben, Exceptional field theory. III. E 8(8), Phys. Rev. D 90 (2014) 066002 [arXiv:1406.3348] [INSPIRE].
  98. [98]
    E. Musaev and H. Samtleben, Fermions and supersymmetry in E 6(6) exceptional field theory, JHEP 03 (2015) 027 [arXiv:1412.7286] [INSPIRE].ADSCrossRefGoogle Scholar
  99. [99]
    O. Hohm and Y.-N. Wang, Tensor hierarchy and generalized Cartan calculus in SL(3) × SL(2) exceptional field theory, JHEP 04 (2015) 050 [arXiv:1501.01600] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  100. [100]
    A. Abzalov, I. Bakhmatov and E.T. Musaev, Exceptional field theory: SO(5, 5), JHEP 06 (2015) 088 [arXiv:1504.01523] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  101. [101]
    E.T. Musaev, Exceptional field theory: SL(5), JHEP 02 (2016) 012 [arXiv:1512.02163] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  102. [102]
    D.S. Berman, C.D.A. Blair, E. Malek and F.J. Rudolph, An action for F-theory: SL(2) + exceptional field theory, Class. Quant. Grav. 33 (2016) 195009 [arXiv:1512.06115] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  103. [103]
    F. Ciceri, A. Guarino and G. Inverso, The exceptional story of massive IIA supergravity, JHEP 08 (2016) 154 [arXiv:1604.08602] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  104. [104]
    A. Baguet and H. Samtleben, E 8(8) Exceptional Field Theory: Geometry, Fermions and Supersymmetry, JHEP 09 (2016) 168 [arXiv:1607.03119] [INSPIRE].ADSCrossRefGoogle Scholar
  105. [105]
    A. Coimbra, C. Strickland-Constable and D. Waldram, Supergravity as Generalised Geometry II: E d(d) ×  + and M-theory, JHEP 03 (2014) 019 [arXiv:1212.1586] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  106. [106]
    G. Aldazabal, W. Baron, D. Marques and C. Núñez, The effective action of Double Field Theory, JHEP 11 (2011) 052 [Erratum ibid. 1111 (2011) 109] [arXiv:1109.0290] [INSPIRE].
  107. [107]
    D. Geissbuhler, Double Field Theory and N = 4 Gauged Supergravity, JHEP 11 (2011) 116 [arXiv:1109.4280] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  108. [108]
    M. Graña and D. Marques, Gauged Double Field Theory, JHEP 04 (2012) 020 [arXiv:1201.2924] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  109. [109]
    O. Hohm and H. Samtleben, Consistent Kaluza-Klein Truncations via Exceptional Field Theory, JHEP 01 (2015) 131 [arXiv:1410.8145] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Yuho Sakatani
    • 1
    • 2
    Email author
  • Shozo Uehara
    • 1
  • Kentaroh Yoshida
    • 3
  1. 1.Department of PhysicsKyoto Prefectural University of MedicineKyotoJapan
  2. 2.Fields, Gravity and Strings, CTPUInstitute for Basic SciencesDaejeonKorea
  3. 3.Department of PhysicsKyoto UniversityKyotoJapan

Personalised recommendations