Advertisement

Moduli stabilization and the holographic RG for AdS and dS

  • Xi Dong
  • Bart Horn
  • Eva Silverstein
  • Gonzalo Torroba
Open Access
Article

Abstract

We relate moduli stabilization (V = 0) in the bulk of AdS D or dS D to basic properties of the Wilsonian effective action in the holographic dual theory on dSD−1: the single-trace terms in the action have vanishing beta functions, and higher-trace couplings are determined purely from lower-trace ones. In the de Sitter case, this encodes the maximal symmetry of the bulk spacetime in a quantity which is accessible within an observer patch. Along the way, we clarify the role of counterterms, constraints, and operator redundancy in the Wilsonian holographic RG prescription, reproducing the expected behavior of the trace of the stress-energy tensor in the dual for both AdSD and dSD . We further show that metastability of the gravity-side potential energy corresponds to a nonperturbatively small imaginary contribution to the Wilsonian action of pure de Sitter, a result consistent with the need for additional degrees of freedom in the holographic description of its ultimate decay.

Keywords

Gauge-gravity correspondence AdS-CFT Correspondence Renormalization Group 

References

  1. [1]
    M. Alishahiha, A. Karch, E. Silverstein and D. Tong, The dS/dS correspondence, AIP Conf. Proc. 743 (2005) 393 [hep-th/0407125] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    M. Alishahiha, A. Karch and E. Silverstein, Hologravity, JHEP 06 (2005) 028 [hep-th/0504056] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  3. [3]
    X. Dong, B. Horn, E. Silverstein and G. Torroba, Micromanaging de Sitter holography, Class. Quant. Grav. 27 (2010) 245020 [arXiv:1005.5403] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  4. [4]
    X. Dong, B. Horn, S. Matsuura, E. Silverstein and G. Torroba, FRW solutions and holography from uplifted AdS/CFT, Phys. Rev. D 85 (2012) 104035 [arXiv:1108.5732] [INSPIRE].ADSGoogle Scholar
  5. [5]
    D. Anninos, S.A. Hartnoll and D.M. Hofman, Static patch solipsism: conformal symmetry of the de Sitter worldline, Class. Quant. Grav. 29 (2012) 075002 [arXiv:1109.4942] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    D. Anninos, T. Hartman and A. Strominger, Higher spin realization of the dS/CFT correspondence, arXiv:1108.5735 [INSPIRE].
  7. [7]
    A. Strominger, Inflation and the dS/CFT correspondence, JHEP 11 (2001) 049 [hep-th/0110087] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  8. [8]
    A. Strominger, The dS/CFT correspondence, JHEP 10 (2001) 034 [hep-th/0106113] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  9. [9]
    D. Harlow and L. Susskind, Crunches, hats and a conjecture, arXiv:1012.5302 [INSPIRE].
  10. [10]
    I. Heemskerk and J. Polchinski, Holographic and Wilsonian renormalization groups, JHEP 06 (2011) 031 [arXiv:1010.1264] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  11. [11]
    P. Mansfield and D. Nolland, One loop conformal anomalies from AdS/CFT in the Schrödinger representation, JHEP 07 (1999) 028 [hep-th/9906054] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    J. de Boer, E.P. Verlinde and H.L. Verlinde, On the holographic renormalization group, JHEP 08 (2000) 003 [hep-th/9912012] [INSPIRE].CrossRefGoogle Scholar
  13. [13]
    M. Li, A note on relation between holographic RG equation and Polchinskis RG equation, Nucl. Phys. B 579 (2000) 525 [hep-th/0001193] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    E.T. Akhmedov and E.T. Musaev, An exact result for Wilsonian and holographic renormalization group, Phys. Rev. D 81 (2010) 085010 [arXiv:1001.4067] [INSPIRE].ADSGoogle Scholar
  15. [15]
    T. Faulkner, H. Liu and M. Rangamani, Integrating out geometry: holographic Wilsonian RG and the membrane paradigm, JHEP 08 (2011) 051 [arXiv:1010.4036] [INSPIRE].MathSciNetADSGoogle Scholar
  16. [16]
    M. Dodelson et al., work in progress.Google Scholar
  17. [17]
    B. Freivogel, Y. Sekino, L. Susskind and C.-P. Yeh, A holographic framework for eternal inflation, Phys. Rev. D 74 (2006) 086003 [hep-th/0606204] [INSPIRE].MathSciNetADSGoogle Scholar
  18. [18]
    K.G. Wilson, The renormalization group and critical phenomena, Rev. Mod. Phys. 55 (1983) 583 [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    J. Polchinski, Renormalization and effective Lagrangians, Nucl. Phys. B 231 (1984) 269 [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    C. Wetterich, Exact evolution equation for the effective potential, Phys. Lett. B 301 (1993) 90 [INSPIRE].ADSGoogle Scholar
  21. [21]
    M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  22. [22]
    D. Harlow and D. Stanford, Operator dictionaries and wave functions in AdS/CFT and dS/CFT, arXiv:1104.2621 [INSPIRE].
  23. [23]
    S. Kachru and E. Silverstein, 4-D conformal theories and strings on orbifolds, Phys. Rev. Lett. 80 (1998) 4855 [hep-th/9802183] [INSPIRE].MathSciNetADSzbMATHCrossRefGoogle Scholar
  24. [24]
    A. Dymarsky, I.R. Klebanov and R. Roiban, Perturbative search for fixed lines in large-N gauge theories, JHEP 08 (2005) 011 [hep-th/0505099] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  25. [25]
    S. Kachru, D. Simic and S.P. Trivedi, Stable non-supersymmetric throats in string theory, JHEP 05 (2010) 067 [arXiv:0905.2970] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  26. [26]
    A. Hamilton, D.N. Kabat, G. Lifschytz and D.A. Lowe, Local bulk operators in AdS/CFT: a boundary view of horizons and locality, Phys. Rev. D 73 (2006) 086003 [hep-th/0506118] [INSPIRE].MathSciNetADSGoogle Scholar
  27. [27]
    I. Heemskerk, D. Marolf, J. Polchinski and J. Sully, Bulk and transhorizon measurements in AdS/CFT, JHEP 10 (2012) 165 [arXiv:1201.3664] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    P. Breitenlohner and D.Z. Freedman, Positive energy in anti-de Sitter backgrounds and gauged extended supergravity, Phys. Lett. B 115 (1982) 197 [INSPIRE].MathSciNetADSGoogle Scholar
  29. [29]
    P. Breitenlohner and D.Z. Freedman, Stability in gauged extended supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].MathSciNetADSzbMATHCrossRefGoogle Scholar
  30. [30]
    S. Coleman, Aspects of symmetry: selected Erice lectures, Cambridge University Press, Cambridge U.K. (1988).Google Scholar
  31. [31]
    D. Anninos, T. Anous, I. Bredberg and G.S. Ng, Incompressible fluids of the de Sitter horizon and beyond, JHEP 05 (2012) 107 [arXiv:1110.3792] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    D. Anninos, De Sitter musings, Int. J. Mod. Phys. A 27 (2012) 1230013 [arXiv:1205.3855] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  33. [33]
    R. Bousso and I.-S. Yang, Globallocal duality in eternal inflation, Phys. Rev. D 80 (2009) 124024 [arXiv:0904.2386] [INSPIRE].MathSciNetADSGoogle Scholar
  34. [34]
    D. Harlow, S.H. Shenker, D. Stanford and L. Susskind, Tree-like structure of eternal inflation: a solvable model, Phys. Rev. D 85 (2012) 063516 [arXiv:1110.0496] [INSPIRE].ADSGoogle Scholar

Copyright information

© SISSA 2013

Authors and Affiliations

  • Xi Dong
    • 1
    • 2
  • Bart Horn
    • 1
    • 2
    • 3
  • Eva Silverstein
    • 1
    • 2
  • Gonzalo Torroba
    • 1
    • 2
  1. 1.Stanford Institute for Theoretical Physics, Department of PhysicsStanford UniversityStanfordU.S.A
  2. 2.Theory Group, SLAC National Accelerator LaboratoryMenlo ParkU.S.A
  3. 3.Physics Department and Institute for Strings, Cosmology and Astroparticle PhysicsColumbia UniversityNew YorkU.S.A

Personalised recommendations