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Chiral matter wavefunctions in warped compactifications

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Abstract

We analyze the wavefunctions for open strings stretching between intersecting 7-branes in type IIB/F-theory warped compactifications, as a first step in understanding the warped effective field theory of 4d chiral fermions. While in general the equations of motion do not seem to admit a simple analytic solution, we provide a method for solving the wavefunctions in the case of weak warping. The method describes warped zero modes as a perturbative expansion in the unwarped spectrum, the coefficients of the expansion depending on the warping. We perform our analysis with and without the presence of worldvolume fluxes, illustrating the procedure with some examples. Finally, we comment on the warped effective field theory for the modes at the intersection.

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References

  1. N. Arkani-Hamed, S. Dimopoulos and G.R. Dvali, The hierarchy problem and new dimensions at a millimeter, Phys. Lett. B 429 (1998) 263 [hep-ph/9803315] [SPIRES].

    ADS  Google Scholar 

  2. I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos and G.R. Dvali, New dimensions at a millimeter to a Fermi and superstrings at a TeV, Phys. Lett. B 436 (1998) 257 [hep-ph/9804398] [SPIRES].

    ADS  Google Scholar 

  3. G. Shiu and S.H. Henry Tye, TeV scale superstring and extra dimensions, Phys. Rev. D 58 (1998) 106007 [hep-th/9805157] [SPIRES].

    ADS  Google Scholar 

  4. I. Antoniadis, A possible new dimension at a few TeV, Phys. Lett. B 246 (1990) 377 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  5. J.D. Lykken, W eak scale superstrings, Phys. Rev. D 54 (1996) 3693 [hep-th/9603133] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  6. 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] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  7. J.P. Conlon, F. Quevedo and K. Suruliz, Large-volume flux compactifications: moduli spectrum and D3/D7 soft supersymmetry breaking, JHEP 08 (2005) 007 [hep-th/0505076] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  8. J.P. Conlon, Moduli stabilisation and applications in IIB string theory, Fortsch. Phys. 55 (2007) 287 [hep-th/0611039] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  9. L. Randall and R. Sundrum, A large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370 [hep-ph/9905221] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. H.L. Verlinde, Holography and compactification, Nucl. Phys. B 580 (2000) 264 [hep-th/9906182] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  11. K. Dasgupta, G. Rajesh and S. Sethi, M theory, orientifolds and G-flux, JHEP 08 (1999) 023 [hep-th/9908088] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  12. B.R. Greene, K. Schalm and G. Shiu, Warped compactifications in M and F-theory, Nucl. Phys. B 584 (2000) 480 [hep-th/0004103] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  13. K. Becker and M. Becker, M-theory on eight-manifolds, Nucl. Phys. B 477 (1996) 155 [hep-th/9605053] [SPIRES].

    Article  ADS  Google Scholar 

  14. K. Becker and M. Becker, Compactifying M-theory to four dimensions, JHEP 11 (2000) 029 [hep-th/0010282] [SPIRES].

    Article  ADS  Google Scholar 

  15. S.B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66 (2002) 106006 [hep-th/0105097] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  16. M.R. Douglas and S. Kachru, Flux compactification, Rev. Mod. Phys. 79 (2007) 733 [hep-th/0610102] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. R. Blumenhagen, B. Körs, D. Lüst and S. Stieberger, Four-dimensional string compactifications with D-branes, orientifolds and fluxes, Phys. Rept. 445 (2007) 1 [hep-th/0610327] [SPIRES].

    Article  ADS  Google Scholar 

  18. M. Graña, Flux compactifications in string theory: a comprehensive review, Phys. Rept. 423 (2006) 91 [hep-th/0509003] [SPIRES].

    Article  ADS  Google Scholar 

  19. S. Kachru et al., Towards inflation in string theory, JCA P 10 (2003) 013 [hep-th/0308055] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  20. A.D. Linde, Inflation and string cosmology, eConf C 040802 (2004) L024 [J. Phys. Conf. Ser. 24 (2005) 151] [Prog. Theor. Phys. Suppl. 163 (2006) 295] [hep-th/0503195] [SPIRES].

    Google Scholar 

  21. J.M. Cline, String cosmology, hep-th/0612129 [SPIRES].

  22. R. Kallosh, On inflation in string theory, Lect. Notes Phys. 738 (2008) 119 [hep-th/0702059] [SPIRES].

    Article  ADS  Google Scholar 

  23. C.P. Burgess, Lectures on cosmic inflation and its potential stringy realizations, Class. Quant. Grav. 24 (2007) S795 [PoS(P2GC)008] [PoS(CARGESE2007)003] [arXiv:0708.2865] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  24. L. McAllister and E. Silverstein, String cosmology: a review, Gen. Rel. Grav. 40 (2008) 565 [arXiv:0710.2951] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  25. D. Baumann and L. McAllister, Advances in inflation in string theory, Ann. Rev. Nucl. Part. Sci. 59 (2009) 67 [arXiv:0901.0265] [SPIRES].

    Article  ADS  Google Scholar 

  26. 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] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  27. J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [SPIRES].

    Article  MathSciNet  MATH  Google Scholar 

  28. S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  29. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [SPIRES].

    MathSciNet  MATH  Google Scholar 

  30. R.R. Metsaev and A.A. Tseytlin, Type IIB superstring action in AdS 5 × S 5 background, Nucl. Phys. B 533 (1998) 109 [hep-th/9805028] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  31. R.R. Metsaev, Type IIB Green-Schwarz superstring in plane wave Ramond-Ramond background, Nucl. Phys. B 625 (2002) 70 [hep-th/0112044] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  32. 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] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  33. A.R. Frey and A. Maharana, Warped spectroscopy: localization of frozen bulk modes, JHEP 08 (2006) 021 [hep-th/0603233] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  34. C.P. Burgess et al., Warped supersymmetry breaking, JHEP 04 (2008) 053 [hep-th/0610255] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  35. M.R. Douglas and G. Torroba, Kinetic terms in warped compactifications, JHEP 05 (2009) 013 [arXiv:0805.3700] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  36. G. Shiu, G. Torroba, B. Underwood and M.R. Douglas, Dynamics of warped flux compactifications, JHEP 06 (2008) 024 [arXiv:0803.3068] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  37. A.R. Frey, G. Torroba, B. Underwood and M.R. Douglas, The universal Kähler modulus in warped compactifications, JHEP 01 (2009) 036 [arXiv:0810.5768] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  38. L. Martucci, On moduli and effective theory of \( \mathcal{N} = 1 \) warped flux compactifications, JHEP 05 (2009) 027 [arXiv:0902.4031] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  39. B. Underwood, A breathing mode for warped compactifications, arXiv:1009.4200 [SPIRES].

  40. F. Marchesano, P. McGuirk and G. Shiu, Open string wavefunctions in warped compactifications, JHEP 04 (2009) 095 [arXiv:0812.2247] [SPIRES].

    Article  ADS  Google Scholar 

  41. H.-Y. Chen, Y. Nakayama and G. Shiu, On D3-brane dynamics at strong warping, Int. J. Mod. Phys. A 25 (2010) 2493 [arXiv:0905.4463] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  42. L. Martucci, J. Rosseel, D. Van den Bleeken and A. Van Proeyen, Dirac actions for D-branes on backgrounds with fluxes, Class. Quant. Grav. 22 (2005) 2745 [hep-th/0504041] [SPIRES].

    Article  ADS  MATH  Google Scholar 

  43. S.H. Katz and C. Vafa, Matter from geometry, Nucl. Phys. B 497 (1997) 146 [hep-th/9606086] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  44. K. Hashimoto and S. Nagaoka, Recombination of intersecting D-branes by local tachyon condensation, JHEP 06 (2003) 034 [hep-th/0303204] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  45. S. Nagaoka, Higher dimensional recombination of intersecting D-branes, JHEP 02 (2004) 063 [hep-th/0312010] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  46. D. Cremades, L.E. Ibáñez and F. Marchesano, Computing Yukawa couplings from magnetized extra dimensions, JHEP 05 (2004) 079 [hep-th/0404229] [SPIRES].

    Article  ADS  Google Scholar 

  47. A. Butti et al., On the geometry and the moduli space of β-deformed quiver gauge theories, JHEP 07 (2008) 053 [arXiv:0712.1215] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  48. R.C. Myers, Dielectric-branes, JHEP 12 (1999) 022 [hep-th/9910053] [SPIRES].

    Article  ADS  Google Scholar 

  49. H. Jockers and J. Louis, D-terms and F-terms from D7-brane fluxes, Nucl. Phys. B 718 (2005) 203 [hep-th/0502059] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  50. L. Martucci, D-branes on general \( \mathcal{N} = 1 \) backgrounds: superpotentials and D-terms, JHEP 06 (2006) 033 [hep-th/0602129] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  51. M. Mariño, R. Minasian, G.W. Moore and A. Strominger, Nonlinear instantons from supersymmetric p-branes, JHEP 01 (2000) 005 [hep-th/9911206] [SPIRES].

    Article  ADS  Google Scholar 

  52. J. Gomis, F. Marchesano and D. Mateos, An open string landscape, JHEP 11 (2005) 021 [hep-th/0506179] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  53. L. Martucci and P. Smyth, Supersymmetric D-branes and calibrations on general \( \mathcal{N} = 1 \) backgrounds, JHEP 11 (2005) 048 [hep-th/0507099] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  54. R. Blumenhagen, M. Cvetič, P. Langacker and G. Shiu, Toward realistic intersecting D-brane models, Ann. Rev. Nucl. Part. Sci. 55 (2005) 71 [hep-th/0502005] [SPIRES].

    Article  ADS  Google Scholar 

  55. C. Beasley, J.J. Heckman and C. Vafa, GUTs and exceptional branes in F-theory — I, JHEP 01 (2009) 058 [arXiv:0802.3391] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  56. S. Cecotti, M.C.N. Cheng, J.J. Heckman and C. Vafa, Yukawa couplings in F-theory and non-commutative geometry, arXiv:0910.0477 [SPIRES].

  57. R. Donagi and M. Wijnholt, Model building with F-theory, arXiv:0802.2969 [SPIRES].

  58. A. Font and L.E. Ibáñez, Matter wave functions and Yukawa couplings in F-theory grand unification, JHEP 09 (2009) 036 [arXiv:0907.4895] [SPIRES].

    Article  ADS  Google Scholar 

  59. J.P. Conlon and E. Palti, Aspects of flavour and supersymmetry in F-theory GUTs, JHEP 01 (2010) 029 [arXiv:0910.2413] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  60. G.K. Leontaris and G.G. Ross, Yukawa couplings and fermion mass structure in F-theory GUTs, JHEP 02 (2011) 108 [arXiv:1009.6000] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  61. J.P. Conlon, A. Maharana and F. Quevedo, Wave functions and Yukawa couplings in local string compactifications, JHEP 09 (2008) 104 [arXiv:0807.0789] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  62. P.G. Cámara and F. Marchesano, Open string wavefunctions in flux compactifications, JHEP 10 (2009) 017 [arXiv:0906.3033] [SPIRES].

    Article  Google Scholar 

  63. P.G. Cámara and F.G. Marchesano, Physics from open string wavefunctions, PoS(EPS-HEP 2009)390 [SPIRES].

  64. M. Graña and J. Polchinski, Supersymmetric three-form flux perturbations on AdS 5, Phys. Rev. D 63 (2001) 026001 [hep-th/0009211] [SPIRES].

    ADS  Google Scholar 

  65. S.S. Gubser, Supersymmetry and F-theory realization of the deformed conifold with three-form flux, hep-th/0010010 [SPIRES].

  66. M. Graña and J. Polchinski, Gauge/gravity duals with holomorphic dilaton, Phys. Rev. D 65 (2002) 126005 [hep-th/0106014] [SPIRES].

    ADS  Google Scholar 

  67. C. Vafa, Evidence for F-theory, Nucl. Phys. B 469 (1996) 403 [hep-th/9602022] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  68. D.R. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau threefolds — I, Nucl. Phys. B 473 (1996) 74 [hep-th/9602114] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  69. D.R. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau threefolds — II, Nucl. Phys. B 476 (1996) 437 [hep-th/9603161] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  70. M. Bershadsky et al., Geometric singularities and enhanced gauge symmetries, Nucl. Phys. B 481 (1996) 215 [hep-th/9605200] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  71. D. Lüst, F. Marchesano, L. Martucci and D. Tsimpis, Generalized non-supersymmetric flux vacua, JHEP 11 (2008) 021 [arXiv:0807.4540] [SPIRES].

    Article  Google Scholar 

  72. M. Berkooz, M.R. Douglas and R.G. Leigh, Branes intersecting at angles, Nucl. Phys. B 480 (1996) 265 [hep-th/9606139] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  73. N.S. Manton, Fermions and parity violation in dimensional reduction schemes, Nucl. Phys. B 193 (1981) 502 [SPIRES].

    Article  ADS  Google Scholar 

  74. G. Chapline and R. Slansky, Dimensional reduction and flavor chirality, Nucl. Phys. B 209 (1982) 461 [SPIRES].

    Article  ADS  Google Scholar 

  75. S. Randjbar-Daemi, A. Salam and J.A. Strathdee, Spontaneous compactification in six-dimensional Einstein-Maxwell theory, Nucl. Phys. B 214 (1983) 491 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  76. C. Wetterich, Dimensional reduction of Weyl, Majorana and Majorana-Weyl spinors, Nucl. Phys. B 222 (1983) 20 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  77. P.H. Frampton and K. Yamamoto, Unitary flavor unification through higher dimensions, Phys. Rev. Lett. 52 (1984) 2016 [SPIRES].

    Article  ADS  Google Scholar 

  78. P.H. Frampton and T.W. Kephart, Left-right asymmetry from the eight sphere, Phys. Rev. Lett. 53 (1984) 867 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  79. E. Witten, Fermion quantum numbers in Kaluza-Klein theory, lecture given at Shelter Island II Conf., Shelter Island U.S.A. June 1–2 1983 [SPIRES].

  80. E. Witten, Some properties of O(32) superstrings, Phys. Lett. B 149 (1984) 351 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  81. K. Pilch and A.N. Schellekens, Symmetric vacua of higher dimensional Einstein Yang-Mills theories, Nucl. Phys. B 256 (1985) 109 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  82. K. Pilch and A.N. Schellekens, Do quarks know about Kähler metrics?, Phys. Lett. B 164 (1985) 31 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  83. L. Aparicio, A. Font, L.E. Ibáñez and F. Marchesano, Flux and instanton effects in local F-theory models and hierarchical fermion masses, arXiv:1104.2609 [SPIRES].

  84. D. Marolf, L. Martucci and P.J. Silva, Fermions, T-duality and effective actions for D-branes in bosonic backgrounds, JHEP 04 (2003) 051 [hep-th/0303209] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  85. D. Marolf, L. Martucci and P.J. Silva, Actions and fermionic symmetries for D-branes in bosonic backgrounds, JHEP 07 (2003) 019 [hep-th/0306066] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  86. B. Wynants, Supersymmetric actions for multiple D-branes on D-brane backgrounds, master’s thesis, Katholieke Universiteit Leuven, Leuven Belgium (2006).

  87. L.E. Ibáñez, C. Muñoz and S. Rigolin, Aspects of type-I string phenomenology, Nucl. Phys. B 553 (1999) 43 [hep-ph/9812397] [SPIRES].

    Article  ADS  Google Scholar 

  88. M. Cvetič and I. Papadimitriou, Conformal field theory couplings for intersecting D-branes on orientifolds, Phys. Rev. D 68 (2003) 046001 [Erratum ibid. D 70 (2004) 029903] [hep-th/0303083] [SPIRES].

    ADS  Google Scholar 

  89. D. Lüst, P. Mayr, R. Richter and S. Stieberger, Scattering of gauge, matter and moduli fields from intersecting branes, Nucl. Phys. B 696 (2004) 205 [hep-th/0404134] [SPIRES].

    Article  ADS  Google Scholar 

  90. D. Lüst, S. Reffert and S. Stieberger, Flux-induced soft supersymmetry breaking in chiral type IIB orientifolds with D3/D7-branes, Nucl. Phys. B 706 (2005) 3 [hep-th/0406092] [SPIRES].

    Article  ADS  Google Scholar 

  91. D. Lüst, S. Reffert and S. Stieberger, MSSM with soft SUSY breaking terms from D7-branes with fluxes, Nucl. Phys. B 727 (2005) 264 [hep-th/0410074] [SPIRES].

    Article  ADS  Google Scholar 

  92. A. Font and L.E. Ibáñez, SUSY-breaking soft terms in a MSSM magnetized D7-brane model, JHEP 03 (2005) 040 [hep-th/0412150] [SPIRES].

    Article  ADS  Google Scholar 

  93. M. Bertolini, M. Billó, A. Lerda, J.F. Morales and R. Russo, Brane world effective actions for D-branes with fluxes, Nucl. Phys. B 743 (2006) 1 [hep-th/0512067] [SPIRES].

    Article  ADS  Google Scholar 

  94. F. Marchesano and G. Shiu, MSSM vacua from flux compactifications, Phys. Rev. D 71 (2005) 011701 [hep-th/0408059] [SPIRES].

    ADS  Google Scholar 

  95. F. Marchesano and G. Shiu, Building MSSM flux vacua, JHEP 11 (2004) 041 [hep-th/0409132] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  96. H. Jockers and J. Louis, The effective action of D7-branes in \( \mathcal{N} = 1 \) Calabi-Yau orientifolds, Nucl. Phys. B 705 (2005) 167 [hep-th/0409098] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  97. H. Jockers, The effective action of D-branes in Calabi-Yau orientifold compactifications, Fortsch. Phys. 53 (2005) 1087 [hep-th/0507042] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  98. P.G. Cámara, L.E. Ibáñez and A.M. Uranga, Flux-induced SUSY-breaking soft terms on D7-D3 brane systems, Nucl. Phys. B 708 (2005) 268 [hep-th/0408036] [SPIRES].

    Article  ADS  Google Scholar 

  99. F. Benini et al., Holographic gauge mediation, JHEP 12 (2009) 031 [arXiv:0903.0619] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  100. P. McGuirk, G. Shiu and Y. Sumitomo, Holographic gauge mediation via strongly coupled messengers, Phys. Rev. D 81 (2010) 026005 [arXiv:0911.0019] [SPIRES].

    ADS  Google Scholar 

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Marchesano, F., McGuirk, P. & Shiu, G. Chiral matter wavefunctions in warped compactifications. J. High Energ. Phys. 2011, 90 (2011). https://doi.org/10.1007/JHEP05(2011)090

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