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On KKLT/CFT and LVS/CFT dualities

A preprint version of the article is available at arXiv.

Abstract

We present a general discussion of the properties of three dimensional CFT duals to the AdS string theory vacua coming from type IIB Calabi-Yau flux compactifi-cations. Both KKLT and Large Volume Scenario (LVS) minima are considered. In both cases we identify the large ‘central charge’, find a separation of scales between the radius of AdS and the size of the extra dimensions and show that the dual CFT has only a limited number of operators with small conformal dimension. Differences between the two sets of duals are identified. Besides a different amount of supersymmetry (\( \mathcal{N}=1 \) for KKLT and \( \mathcal{N}=0 \) for LVS) we find that the LVS CFT dual has only one scalar operator with O(1) conformal dimension, corresponding to the volume modulus, whereas in KKLT the whole set of h1,1 Kähler moduli have this property. Also, the maximal number of degrees of freedom is estimated to be larger in LVS than in KKLT duals. In both cases we explic-itly compute the coefficient of the logarithmic contribution to the one-loop vacuum energy which should be invariant under duality and therefore provides a non-trivial prediction for the dual CFT. This coefficient takes a particularly simple form in the KKLT case.

References

  1. 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] [INSPIRE].

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

    ADS  MathSciNet  Article  MATH  Google Scholar 

  3. O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  4. J. Polchinski, Introduction to gauge/gravity duality, arXiv:1010.6134 [INSPIRE].

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

    ADS  MathSciNet  Article  Google Scholar 

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

    ADS  MathSciNet  Article  MATH  Google Scholar 

  7. 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] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

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

    ADS  MathSciNet  Article  MATH  Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

  10. 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].

    ADS  MathSciNet  MATH  Google Scholar 

  11. M.R. Douglas, The statistics of string/M theory vacua, JHEP 05 (2003) 046 [hep-th/0303194] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  12. S. Ashok and M.R. Douglas, Counting flux vacua, JHEP 01 (2004) 060 [hep-th/0307049] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  13. F. Denef, M.R. Douglas and B. Florea, Building a better racetrack, JHEP 06 (2004) 034 [hep-th/0404257] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  14. F. Denef and M.R. Douglas, Distributions of flux vacua, JHEP 05 (2004) 072 [hep-th/0404116] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  15. F. Denef and M.R. Douglas, Distributions of nonsupersymmetric flux vacua, JHEP 03 (2005) 061 [hep-th/0411183] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  16. B.S. Acharya, F. Denef and R. Valandro, Statistics of M-theory vacua, JHEP 06 (2005) 056 [hep-th/0502060] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  17. E. Silverstein, AdS and dS entropy from string junctions: or, the function of junction conjunctions, in From fields to strings, volume 3, M. Shifman ed., World Scientific, Singapore (2003), hep-th/0308175 [INSPIRE].

  18. J. Polchinski and E. Silverstein, Dual purpose landscaping tools: small extra dimensions in AdS/CFT, arXiv:0908.0756 [INSPIRE].

  19. T. Banks, Landskepticism or why effective potentials dont count string models, hep-th/0412129 [INSPIRE].

  20. C. Vafa, The String landscape and the swampland, hep-th/0509212 [INSPIRE].

  21. O. Aharony, Y.E. Antebi and M. Berkooz, On the conformal field theory duals of type IIA AdS4 flux compactifications, JHEP 02 (2008) 093 [arXiv:0801.3326] [INSPIRE].

    ADS  Article  Google Scholar 

  22. F. Denef and S.A. Hartnoll, Landscape of superconducting membranes, Phys. Rev. D 79 (2009) 126008 [arXiv:0901.1160] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  23. G. Torroba and H. Wang, Black branes in flux compactifications, JHEP 10 (2013) 126 [arXiv:1306.3982] [INSPIRE].

    ADS  Article  Google Scholar 

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

    ADS  MathSciNet  Article  MATH  Google Scholar 

  25. 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].

    ADS  MathSciNet  Article  Google Scholar 

  26. 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] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  27. S. de Alwis, R. Gupta, E. Hatefi and F. Quevedo, Stability, tunneling and flux changing de Sitter transitions in the large volume string scenario, JHEP 11 (2013) 179 [arXiv:1308.1222] [INSPIRE].

    ADS  Article  Google Scholar 

  28. M. Cicoli, S. Krippendorf, C. Mayrhofer, F. Quevedo and R. Valandro, D-branes at del Pezzo singularities: global embedding and moduli stabilisation, JHEP 09 (2012) 019 [arXiv:1206.5237] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  29. J. Louis, M. Rummel, R. Valandro and A. Westphal, Building an explicit de Sitter, JHEP 10 (2012) 163 [arXiv:1208.3208] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  30. M. Cicoli, S. Krippendorf, C. Mayrhofer, F. Quevedo and R. Valandro, D3/D7 branes at singularities: constraints from global embedding and moduli stabilisation, JHEP 07 (2013) 150 [arXiv:1304.0022] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  31. M. Cicoli et al., Explicit de Sitter flux vacua for global string models with chiral matter, JHEP 05 (2014) 001 [arXiv:1312.0014] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  32. S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  33. S. Banerjee, R.K. Gupta and A. Sen, Logarithmic corrections to extremal black hole entropy from quantum entropy function, JHEP 03 (2011) 147 [arXiv:1005.3044] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  34. S. Banerjee, R.K. Gupta, I. Mandal and A. Sen, Logarithmic corrections to N = 4 and N =8 black hole entropy: a one loop test of quantum gravity, JHEP 11 (2011) 143 [arXiv:1106.0080] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  35. A. Sen, Logarithmic corrections to N = 2 black hole entropy: an infrared window into the microstates, arXiv:1108.3842 [INSPIRE].

  36. R.K. Gupta, S. Lal and S. Thakur, Logarithmic corrections to extremal black hole entropy in \( \mathcal{N}=2 \), 4 and 8 supergravity, JHEP 11 (2014) 072[arXiv:1402.2441] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  37. A. Chowdhury, R.K. Gupta, S. Lal, M. Shyani and S. Thakur, Logarithmic corrections to twisted indices from the quantum entropy function, JHEP 11 (2014) 002 [arXiv:1404.6363] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  38. S. Bhattacharyya, A. Grassi, M. Mariño and A. Sen, A one-loop test of quantum supergravity, Class. Quant. Grav. 31 (2014) 015012 [arXiv:1210.6057] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  39. M. Beccaria, G. Macorini and A.A. Tseytlin, Supergravity one-loop corrections on AdS7 and AdS3, higher spins and AdS/CFT, Nucl. Phys. B 892 (2015) 211 [arXiv:1412.0489] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  40. P. Kraus, F. Larsen and S.P. Trivedi, The Coulomb branch of gauge theory from rotating branes, JHEP 03 (1999) 003 [hep-th/9811120] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  41. S. Gukov, C. Vafa and E. Witten, CFTs from Calabi-Yau four folds, Nucl. Phys. B 584 (2000) 69 [Erratum ibid. B 608 (2001) 477] [hep-th/9906070] [INSPIRE].

  42. E. Witten, Nonperturbative superpotentials in string theory, Nucl. Phys. B 474 (1996) 343 [hep-th/9604030] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  43. 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].

    ADS  MathSciNet  Article  Google Scholar 

  44. 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].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  45. S. El-Showk and K. Papadodimas, Emergent spacetime and holographic CFTs, JHEP 10 (2012) 106 [arXiv:1101.4163] [INSPIRE].

    ADS  Article  Google Scholar 

  46. J.L. Cardy, Anisotropic corrections to correlation functions in finite size systems, Nucl. Phys. B 290 (1987) 355 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  47. P. Kovtun and A. Ritz, Black holes and universality classes of critical points, Phys. Rev. Lett. 100 (2008) 171606 [arXiv:0801.2785] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  48. M. Cicoli, J.P. Conlon, A. Maharana and F. Quevedo, A note on the magnitude of the flux superpotential, JHEP 01 (2014) 027 [arXiv:1310.6694] [INSPIRE].

    ADS  Article  Google Scholar 

  49. D. Martinez-Pedrera, D. Mehta, M. Rummel and A. Westphal, Finding all flux vacua in an explicit example, JHEP 06 (2013) 110 [arXiv:1212.4530] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  50. 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].

    ADS  Article  MATH  Google Scholar 

  51. E. Witten, Baryons and branes in Anti-de Sitter space, JHEP 07 (1998) 006 [hep-th/9805112] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  52. S.S. Gubser and I.R. Klebanov, Baryons and domain walls in an N = 1 superconformal gauge theory, Phys. Rev. D 58 (1998) 125025 [hep-th/9808075] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  53. K. Papadodimas, AdS/CFT and the cosmological constant problem, arXiv:1106.3556 [INSPIRE].

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

    ADS  Article  MATH  Google Scholar 

  55. S.M. Christensen and M.J. Duff, New gravitational index theorems and supertheorems, Nucl. Phys. B 154 (1979) 301 [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  56. D.V. Vassilevich, Heat kernel expansion: Users manual, Phys. Rept. 388 (2003) 279 [hep-th/0306138] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  57. D.E. Diaz and H. Dorn, Partition functions and double-trace deformations in AdS/CFT, JHEP 05 (2007) 046 [hep-th/0702163] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  58. B. de Wit and I. Herger, Anti-de Sitter supersymmetry, Lect. Notes Phys. 541 (2000) 79 [hep-th/9908005] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  59. A. Collinucci, F. Denef and M. Esole, D-brane deconstructions in IIB orientifolds, JHEP 02 (2009) 005 [arXiv:0805.1573] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  60. A. Collinucci, M. Kreuzer, C. Mayrhofer and N.-O. Walliser, Four-modulusSwiss Cheesechiral models, JHEP 07 (2009) 074 [arXiv:0811.4599] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  61. M. Cicoli, C. Mayrhofer and R. Valandro, Moduli stabilisation for chiral global models, JHEP 02 (2012) 062 [arXiv:1110.3333] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  62. P. Berglund and I. Garcia-Etxebarria, D-brane instantons on non-Spin cycles, JHEP 01 (2013) 056 [arXiv:1210.1221] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  63. S.M. Christensen and M.J. Duff, Quantizing gravity with a cosmological constant, Nucl. Phys. B 170 (1980) 480 [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  64. D. Hoover and C.P. Burgess, Ultraviolet sensitivity in higher dimensions, JHEP 01 (2006) 058 [hep-th/0507293] [INSPIRE].

    ADS  Article  Google Scholar 

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Correspondence to Roberto Valandro.

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de Alwis, S., Gupta, R.K., Quevedo, F. et al. On KKLT/CFT and LVS/CFT dualities. J. High Energ. Phys. 2015, 36 (2015). https://doi.org/10.1007/JHEP07(2015)036

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Keywords

  • Flux compactifications
  • AdS-CFT Correspondence
  • Gauge-gravity correspon-dence