Skip to main content
SpringerLink
Log in

Aspects of AdS/BCFT

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

A bstract

We expand the results of arXiv:1105.5165, where a holographic description of a conformal field theory defined on a manifold with boundaries (so called BCFT) was proposed, based on AdS/CFT. We construct gravity duals of conformal field theories on strips, balls and also time-dependent boundaries. We show a holographic g-theorem in any dimension. As a special example, we can define a ‘boundary central charge’ in three dimensional conformal field theories and our holographic g-theorem argues that it decreases under RG flows. We also computed holographic one-point functions and confirmed that their scaling property agrees with field theory calculations. Finally, we give an example of string theory embedding of this holography by inserting orientifold 8-planes in AdS4 × CP3.

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. G. ’t Hooft, Dimensional reduction in quantum gravity, gr-qc/9310026 [INSPIRE].

  2. L. Susskind, The World as a hologram, J. Math. Phys. 36 (1995) 6377 [hep-th/9409089] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1133] [hep-th/9711200] [INSPIRE]

    MathSciNet  ADS  MATH  Google Scholar 

  4. 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] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  8. 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 

  9. 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 

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

    Article  ADS  MathSciNet  Google Scholar 

  11. O. Aharony, L. Berdichevsky, M. Berkooz and I. Shamir, Near-horizon solutions for D3-branes ending on 5-branes, arXiv:1106.1870 [INSPIRE].

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

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. G. Compere and D. Marolf, Setting the boundary free in AdS/CFT, Class. Quant. Grav. 25 (2008)195014 [arXiv:0805.1902] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  15. G. Gibbons and S. Hawking, Action Integrals and Partition Functions in Quantum Gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE]

    MathSciNet  ADS  Google Scholar 

  16. J. 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 

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

  18. 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 

  19. 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 

  20. 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 

  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. O. DeWolfe, D.Z. Freedman and H. Ooguri, Holography and defect conformal field theories, Phys. Rev. D 66 (2002) 025009 [hep-th/0111135] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  24. C. Bachas, Asymptotic symmetries of AdS 2 -branes, hep-th/0205115 [INSPIRE].

  25. D. Bak, M. Gutperle and S. Hirano, A Dilatonic deformation of AdS 5 and its field theory dual, JHEP 05 (2003) 072 [hep-th/0304129] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. A. Clark, D. Freedman, A. Karch and M. Schnabl, The Dual of Janus ((<:) ↔ (:>)) an interface CFT, Phys. Rev. D 71 (2005) 066003 [hep-th/0407073] [INSPIRE].

    ADS  Google Scholar 

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

  28. D.E. Berenstein, R. Corrado, W. Fischler and J.M. Maldacena, The Operator product expansion for Wilson loops and surfaces in the large N limit, Phys. Rev. D 59 (1999) 105023 [hep-th/9809188] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  29. P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. 0406 (2004) P06002 [hep-th/0405152] [INSPIRE].

    Article  Google Scholar 

  30. 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 

  31. S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  32. 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 

  33. T. Azeyanagi, A. Karch, T. Takayanagi and E.G. Thompson, Holographic calculation of boundary entropy, JHEP 03 (2008) 054 [arXiv:0712.1850] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  34. M. Chiodaroli, M. Gutperle and L.-Y. Hung, Boundary entropy of supersymmetric Janus solutions, JHEP 09 (2010) 082 [arXiv:1005.4433] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  35. M. Chiodaroli, M. Gutperle, L.-Y. Hung and D. Krym, String Junctions and Holographic Interfaces, Phys. Rev. D 83 (2011) 026003 [arXiv:1010.2758] [INSPIRE].

    ADS  Google Scholar 

  36. M. Bañados, C. Teitelboim and J. Zanelli, The Black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  37. J. 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 

  38. S.W. Hawking and D.N. Page, Thermodynamics of Black Holes in anti-de Sitter Space, Commun. Math. Phys. 87 (1983) 577 [INSPIRE]

    Article  MathSciNet  ADS  Google Scholar 

  39. E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].

    MathSciNet  MATH  Google Scholar 

  40. 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 

  41. 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 

  42. 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 

  43. 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 

  44. S. Yamaguchi, Holographic RG flow on the defect and g theorem, JHEP 10 (2002) 002 [hep-th/0207171] [INSPIRE].

    Article  ADS  Google Scholar 

  45. 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 

  46. J.M. Maldacena, Eternal black holes in anti-de Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  47. V.E. Hubeny, M. Rangamani and T. Takayanagi, A Covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  48. G. Galloway, K. Schleich, D. Witt and E. Woolgar, The AdS/CFT correspondence conjecture and topological censorship, Phys. Lett. B 505 (2001) 255 [hep-th/9912119] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  49. I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  50. O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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

    ADS  Google Scholar 

  52. O. Aharony, O. Bergman and D.L. Jafferis, Fractional M2-branes, JHEP 11 (2008) 043 [arXiv:0807.4924] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  53. D. Gao and K. Hori, On The Structure Of The Chan-Paton Factors For D-branes In Type II Orientifolds, arXiv:1004.3972 [INSPIRE].

  54. M. Fujita, W. Li, S. Ryu and T. Takayanagi, Fractional Quantum Hall Effect via Holography: Chern-Simons, Edge States and Hierarchy, JHEP 06 (2009) 066 [arXiv:0901.0924] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  55. Y. Hikida, W. Li and T. Takayanagi, ABJM with Flavors and FQHE, JHEP 07 (2009) 065 [arXiv:0903.2194] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  56. P. Hořava and E. Witten, Heterotic and type-I string dynamics from eleven-dimensions, Nucl. Phys. B 460 (1996) 506 [hep-th/9510209] [INSPIRE].

    ADS  Google Scholar 

  57. P. Hořava and E. Witten, Eleven-dimensional supergravity on a manifold with boundary, Nucl. Phys. B 475 (1996) 94 [hep-th/9603142] [INSPIRE].

    ADS  Google Scholar 

  58. S.-J. Rey, T. Suyama and S. Yamaguchi, Wilson Loops in Superconformal Chern-Simons Theory and Fundamental Strings in Anti-de Sitter Supergravity Dual, JHEP 03 (2009) 127 [arXiv:0809.3786] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  59. G.V. Dunne, Aspects of Chern-Simons theory, hep-th/9902115 [INSPIRE].

Download references

Author information

Authors and Affiliations

  1. Institute for the Physics and Mathematics of the Universe (IPMU), University of Tokyo, Kashiwa, Chiba, 277-8582, Japan

    Mitsutoshi Fujita & Tadashi Takayanagi

  2. Center for Theoretical Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139, USA

    Erik Tonni

Authors
  1. Mitsutoshi Fujita
    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. Erik Tonni
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Erik Tonni.

Additional information

ArXiv ePrint: 1108.5152

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fujita, M., Takayanagi, T. & Tonni, E. Aspects of AdS/BCFT. J. High Energ. Phys. 2011, 43 (2011). https://doi.org/10.1007/JHEP11(2011)043

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP11(2011)043

K eywords

Search

Navigation