Skip to main content
SpringerLink
Log in

Central charges for BCFTs and holography

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

In this paper, we study the logarithmic terms in the partition functions of CFTs with boundaries (BCFTs). In three dimensions, their coefficients give the boundary central charges, which are conjectured to be monotonically decreasing functions under the RG flows. We present a few supporting evidences from field theory calculations. In two dimensions, we give a holographic construction (AdS/BCFT) for an arbitrary shape of boundary and calculate its logarithmic term as well as boundary energy momentum tensors, confirming its consistency with the Weyl anomaly. Moreover, we give perturbative solutions of gravity duals for the three dimensional BCFTs with any shapes of boundaries. We find that the standard Fefferman-Graham expansion breaks down for generic choices of BCFT boundaries.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

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].

    Article  MathSciNet  MATH  Google Scholar 

  2. 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].

    Article  MathSciNet  ADS  Google Scholar 

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

    MathSciNet  ADS  MATH  Google Scholar 

  4. T. Takayanagi, Holographic dual of BCFT, Phys. Rev. Lett. 107 (2011) 101602 [arXiv:1105.5165] [INSPIRE].

    Article  ADS  Google Scholar 

  5. A. Karch and L. Randall, Locally localized gravity, JHEP 05 (2001) 008 [hep-th/0011156] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. A. Karch and L. Randall, Open and closed string interpretation of SUSY CFT’s on branes with boundaries, JHEP 06 (2001) 063 [hep-th/0105132] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  7. M. Fujita, T. Takayanagi and E. Tonni, Aspects of AdS/BCFT, JHEP 11 (2011) 043 [arXiv:1108.5152] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. I. Affleck and A.W. Ludwig, Universal noninteger ’ground state degeneracy’ in critical quantum systems, Phys. Rev. Lett. 67 (1991) 161 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. D. Friedan and A. Konechny, On the boundary entropy of one-dimensional quantum systems at low temperature, Phys. Rev. Lett. 93 (2004) 030402 [hep-th/0312197] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. Y. Kwon, S. Nam, J.-D. Park and S.-H. Yi, AdS/BCFT correspondence for higher curvature gravity: an example, arXiv:1201.1988 [INSPIRE].

  11. M. Fujita, M. Kaminski and A. Karch, SL(2, \( \mathbb{Z} \)) action on AdS/BCFT and Hall conductivities, arXiv:1204.0012 [INSPIRE].

  12. M. Alishahiha and R. Fareghbal, Boundary CFT from holography, Phys. Rev. D 84 (2011) 106002 [arXiv:1108.5607] [INSPIRE].

    ADS  Google Scholar 

  13. M. Setare and V. Kamali, Two point functions of BCFT, arXiv:1109.3849 [INSPIRE].

  14. M. Setare and V. Kamali, Anti-de Sitter/ boundary conformal field theory correspondence in the nonrelativistic limit, arXiv:1202.4917 [INSPIRE].

  15. T. Takayanagi, Entanglement entropy from a holographic viewpoint, arXiv:1204.2450 [INSPIRE].

  16. O. Aharony, D. Marolf and M. Rangamani, Conformal field theories in Anti-de Sitter space, JHEP 02 (2011) 041 [arXiv:1011.6144] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  17. O. Aharony, L. Berdichevsky, M. Berkooz and I. Shamir, Near-horizon solutions for D3-branes ending on 5-branes, Phys. Rev. D 84 (2011) 126003 [arXiv:1106.1870] [INSPIRE].

    ADS  Google Scholar 

  18. M. Chiodaroli, E. D’Hoker, Y. Guo and M. Gutperle, Exact half-BPS string-junction solutions in six-dimensional supergravity, JHEP 12 (2011) 086 [arXiv:1107.1722] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  19. M. Chiodaroli, E. D’Hoker and M. Gutperle, Simple holographic duals to boundary CFTs, JHEP 02 (2012) 005 [arXiv:1111.6912] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  20. A.M. Garcia-Garcia, J.E. Santos and B. Way, Holographic description of finite size effects in strongly coupled superconductors, arXiv:1204.4189 [INSPIRE].

  21. J.L. Cardy, Conformal invariance and surface critical behavior, Nucl. Phys. B 240 (1984) 514 [INSPIRE].

    Article  ADS  Google Scholar 

  22. D. McAvity and H. Osborn, Conformal field theories near a boundary in general dimensions, Nucl. Phys. B 455 (1995) 522 [cond-mat/9505127] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  23. J.L. Cardy, Boundary conformal field theory, hep-th/0411189 [INSPIRE].

  24. S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  25. S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. T. Nishioka, S. Ryu and T. Takayanagi, Holographic entanglement entropy: an overview, J. Phys. A 42 (2009) 504008 [arXiv:0905.0932] [INSPIRE].

    MathSciNet  Google Scholar 

  27. G. Gibbons and S. Hawking, Action integrals and partition functions in quantum gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  28. M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  29. V. Balasubramanian and P. Kraus, A stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  31. G. Hayward, Gravitational action for space-times with nonsmooth boundaries, Phys. Rev. D 47 (1993) 3275 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  32. R.C. Myers, Stress tensors and Casimir energies in the AdS/CFT correspondence, Phys. Rev. D 60 (1999) 046002 [hep-th/9903203] [INSPIRE].

    ADS  Google Scholar 

  33. J.D. Brown and J.W. York, Quasilocal energy and conserved charges derived from the gravitational action, Phys. Rev. D 47 (1993) 1407 [gr-qc/9209012] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  34. J.D. Brown, S. Lau and J.W. York, Action and energy of the gravitational field, gr-qc/0010024 [INSPIRE].

  35. D. McAvity and H. Osborn, Energy momentum tensor in conformal field theories near a boundary, Nucl. Phys. B 406 (1993) 655 [hep-th/9302068] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  36. J.D. Brown and M. Henneaux, Central charges in the canonical realization of asymptotic symmetries: an example from three-dimensional gravity, Commun. Math. Phys. 104 (1986) 207 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  37. A. Zamolodchikov, Irreversibility of the Flux of the Renormalization Group in a 2D Field Theory, JETP Lett. 43 (1986) 730 [Pisma Zh. Eksp. Teor. Fiz. 43 (1986) 565] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  38. D.L. Jafferis, I.R. Klebanov, S.S. Pufu and B.R. Safdi, Towards the F-theorem: N = 2 field theories on the three-sphere, JHEP 06 (2011) 102 [arXiv:1103.1181] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  39. I.R. Klebanov, S.S. Pufu and B.R. Safdi, F-theorem without supersymmetry, JHEP 10 (2011) 038 [arXiv:1105.4598] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  40. H. Casini and M. Huerta, On the RG running of the entanglement entropy of a circle, arXiv:1202.5650 [INSPIRE].

  41. J.L. Cardy, Is there a c theorem in four-dimensions?, Phys. Lett. B 215 (1988) 749 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  42. D. Freedman, S. Gubser, K. Pilch and N. Warner, Renormalization group flows from holography supersymmetry and a c theorem, Adv. Theor. Math. Phys. 3 (1999) 363 [hep-th/9904017] [INSPIRE].

    MathSciNet  MATH  Google Scholar 

  43. R.C. Myers and A. Sinha, Holographic c-theorems in arbitrary dimensions JHEP 01 (2011) 125 [arXiv:1011.5819] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  44. Z. Komargodski and A. Schwimmer, On renormalization group flows in four dimensions, JHEP 12 (2011) 099 [arXiv:1107.3987] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  45. T.P. Branson, P.B. Gilkey and D.V. Vassilevich, The asymptotics of the laplacian on a manifold with boundary. 2, Boll. Union. Mat. Ital. 11B (1997) 39 [hep-th/9504029] [INSPIRE].

    MathSciNet  Google Scholar 

  46. D. Vassilevich, Heat kernel expansion: user’s manual, Phys. Rept. 388 (2003) 279 [hep-th/0306138] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto, 606-8502, Japan

    Masahiro Nozaki, Tadashi Takayanagi & Tomonori Ugajin

  2. Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa, Chiba, 277-8582, Japan

    Tadashi Takayanagi & Tomonori Ugajin

Authors
  1. Masahiro Nozaki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tadashi Takayanagi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tomonori Ugajin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Masahiro Nozaki.

Additional information

ArXiv ePrint: 1205.1573

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nozaki, M., Takayanagi, T. & Ugajin, T. Central charges for BCFTs and holography. J. High Energ. Phys. 2012, 66 (2012). https://doi.org/10.1007/JHEP06(2012)066

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP06(2012)066

Keywords

Search

Navigation