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Holographic duals of boundary CFTs

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Abstract

New families of regular half-BPS solutions to 6-dimensional Type 4b supergravity with m tensor multiplets are constructed exactly. Their space-time consists of AdS 2 × S 2 warped over a Riemann surface with an arbitrary number of boundary components, and arbitrary genus. The solutions have an arbitrary number of asymptotic AdS 3 × S 3 regions. In addition to strictly single-valued solutions to the supergravity equations whose scalars live in the coset SO(5, m)/SO(5) × SO(m), we also construct stringy solutions whose scalar fields are single-valued up to transformations under the U -duality group SO(5, m; Z), and live in the coset SO(5, m; Z)\SO(5, m)/SO(5) × SO(m). We argue that these Type 4b solutions are holographically dual to general classes of interface and boundary CFTs arising at the juncture of the end-points of 1+1-dimensional bulk CFTs. We evaluate their corresponding holographic entanglement and boundary entropy, and discuss their brane interpretation. We conjecture that the solutions for which Σ has handles and multiple boundaries correspond to the near-horizon limit of half-BPS webs of dyonic strings and three-branes.

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References

  1. 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) 1113] [hep-th/9711200] [INSPIRE].

    MathSciNet  ADS  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].

    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. J.L. Cardy, Boundary Conditions, Fusion Rules and the Verlinde Formula, Nucl. Phys. B 324 (1989) 581 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  5. E. D’Hoker, J. Estes and M. Gutperle, Interface Yang-Mills, supersymmetry and Janus, Nucl. Phys. B 753 (2006) 16 [hep-th/0603013] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. D. Gaiotto and E. Witten, Supersymmetric Boundary Conditions in N = 4 Super Yang-Mills Theory, arXiv:0804.2902 [INSPIRE].

  7. A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152 [hep-th/9611230] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  8. D. Gaiotto and E. Witten, Janus Configurations, Chern-Simons Couplings, And The theta-Angle in N = 4 Super Yang-Mills Theory, JHEP 06 (2010) 097 [arXiv:0804.2907] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. D. Gaiotto and E. Witten, S-duality of Boundary Conditions In N = 4 Super Yang-Mills Theory, Adv. Theor. Math. Phys. 13 (2009) 721 [arXiv:0807.3720] [INSPIRE].

    MathSciNet  MATH  Google Scholar 

  10. B. Assel, C. Bachas, J. Estes and J. Gomis, Holographic Duals of D = 3 N = 4 Superconformal Field Theories, JHEP 08 (2011) 087 [arXiv:1106.4253] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  11. 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 

  12. R. Benichou and J. Estes, Geometry of Open Strings Ending on Backreacting D3-branes, JHEP 03 (2012) 025 [arXiv:1112.3035] [INSPIRE].

    Article  ADS  Google Scholar 

  13. 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 

  14. E. D’Hoker, J. Estes and M. Gutperle, Exact half-BPS Type IIB interface solutions. I. Local solution and supersymmetric Janus, JHEP 06 (2007) 021 [arXiv:0705.0022] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  15. E. D’Hoker, J. Estes and M. Gutperle, Exact half-BPS Type IIB interface solutions. II. Flux solutions and multi-Janus, JHEP 06 (2007) 022 [arXiv:0705.0024] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  16. E. D’Hoker, J. Estes, M. Gutperle and D. Krym, Exact Half-BPS Flux Solutions in M-theory. I: Local Solutions, JHEP 08 (2008) 028 [arXiv:0806.0605] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  17. E. D’Hoker, J. Estes, M. Gutperle and D. Krym, Exact Half-BPS Flux Solutions in M-theory II: Global solutions asymptotic to AdS 7 × S 4, JHEP 12 (2008) 044 [arXiv:0810.4647] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  18. E. D’Hoker, J. Estes, M. Gutperle and D. Krym, Exact Half-BPS Flux Solutions in M-theory III: Existence and rigidity of global solutions asymptotic to AdS 4 × S 7, JHEP 09 (2009) 067 [arXiv:0906.0596] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  19. A. Clark and A. Karch, Super Janus, JHEP 10 (2005) 094 [hep-th/0506265] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  20. J. Gomis and C. Romelsberger, Bubbling Defect CFT’s, JHEP 08 (2006) 050 [hep-th/0604155] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  21. O. Lunin, On gravitational description of Wilson lines, JHEP 06 (2006) 026 [hep-th/0604133] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. O. Lunin, 1/2-BPS states in M-theory and defects in the dual CFTs, JHEP 10 (2007) 014 [arXiv:0704.3442] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  23. S. Yamaguchi, Bubbling geometries for half BPS Wilson lines, Int. J. Mod. Phys. A 22 (2007) 1353 [hep-th/0601089] [INSPIRE].

    ADS  Google Scholar 

  24. J. Gomis and F. Passerini, Holographic Wilson Loops, JHEP 08 (2006) 074 [hep-th/0604007] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  25. J. Kumar and A. Rajaraman, New supergravity solutions for branes in AdS 3 × S 3, Phys. Rev. D 67 (2003) 125005 [hep-th/0212145] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  26. J. Kumar and A. Rajaraman, Supergravity solutions for AdS 3 × S 3 branes, Phys. Rev. D 69 (2004) 105023 [hep-th/0310056] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  27. O. Lunin, Brane webs and 1/4-BPS geometries, JHEP 09 (2008) 028 [arXiv:0802.0735] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  28. E. D’Hoker, J. Estes, M. Gutperle, D. Krym and P. Sorba, Half-BPS supergravity solutions and superalgebras, JHEP 12 (2008) 047 [arXiv:0810.1484] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  29. M. Chiodaroli, M. Gutperle and D. Krym, Half-BPS Solutions locally asymptotic to AdS 3 × S 3 and interface conformal field theories, JHEP 02 (2010) 066 [arXiv:0910.0466] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  30. M. Chiodaroli, E. D’Hoker and M. Gutperle, Open Worldsheets for Holographic Interfaces, JHEP 03 (2010) 060 [arXiv:0912.4679] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  31. 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 

  32. L. Romans, Selfduality for interacting fields: covariant field equations for six-dimensional chiral supergravities, Nucl. Phys. B 276 (1986) 71 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  33. J.H. Schwarz, Lectures on superstring and M-theory dualities, given at ICTP Spring School and at TASI Summer School, Nucl. Phys. Proc. Suppl. 55B (1997) 1 [hep-th/9607201] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  34. K. Dasgupta and S. Mukhi, BPS nature of three string junctions, Phys. Lett. B 423 (1998) 261 [hep-th/9711094] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  35. A. Sen, String network, JHEP 03 (1998) 005 [hep-th/9711130] [INSPIRE].

    Article  ADS  Google Scholar 

  36. 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 

  37. C.G. Callan and J.M. Maldacena, Brane death and dynamics from the Born-Infeld action, Nucl. Phys. B 513 (1998) 198 [hep-th/9708147] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  38. 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 

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

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  41. M. Nozaki, T. Takayanagi and T. Ugajin, Central Charges for BCFTs and Holography, JHEP 06 (2012) 066 [arXiv:1205.1573] [INSPIRE].

    Article  ADS  Google Scholar 

  42. Y. Kwon, S. Nam, J.-D. Park and S.-H. Yi, AdS/BCFT Correspondence for Higher Curvature Gravity: An Example, JHEP 06 (2012) 119 [arXiv:1201.1988] [INSPIRE].

    Article  ADS  Google Scholar 

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

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

    ADS  Google Scholar 

  45. M. Chiodaroli, E. D’Hoker and M. Gutperle, Simple Holographic Duals to Boundary CFTs, JHEP 02 (2012) 005 [arXiv:1111.6912] [INSPIRE].

    Article  ADS  Google Scholar 

  46. C. Bachas and M. Petropoulos, Anti-de Sitter D-branes, JHEP 02 (2001) 025 [hep-th/0012234] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  47. J. Raeymaekers and K. Yogendran, Supersymmetric D-branes in the D1-D5 background, JHEP 12 (2006) 022 [hep-th/0607150] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  48. E. D’Hoker and D. Phong, The Geometry of String Perturbation Theory, Rev. Mod. Phys. 60 (1988) 917 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  49. 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 

  50. 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 

  51. 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 

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

    Article  MathSciNet  ADS  Google Scholar 

  53. 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 

  54. John D. Fay, Theta Functions on Riemann Surfaces, Lect. Notes Math. 352, Springer-Verlag (1973).

  55. O. Aharony, A. Hanany and B. Kol, Webs of (p,q) five-branes, five-dimensional field theories and grid diagrams, JHEP 01 (1998) 002 [hep-th/9710116] [INSPIRE].

    Article  ADS  Google Scholar 

  56. O. Bergman and B. Kol, String webs and 1/4 BPS monopoles, Nucl. Phys. B 536 (1998) 149 [hep-th/9804160] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Institute for Gravitation and the Cosmos, The Pennsylvania State University, University Park, PA, 16802, U.S.A.

    Marco Chiodaroli

  2. Department of Physics and Astronomy, University of California, Los Angeles, CA, 90095, U.S.A.

    Eric D’Hoker & Michael Gutperle

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  1. Marco Chiodaroli
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  2. Eric D’Hoker
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  3. Michael Gutperle
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Correspondence to Michael Gutperle.

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ArXiv ePrint: 1205.5303

This work is supported in part by NSF grants PHY-08-55356 and PHY-07-57702.

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Chiodaroli, M., D’Hoker, E. & Gutperle, M. Holographic duals of boundary CFTs. J. High Energ. Phys. 2012, 177 (2012). https://doi.org/10.1007/JHEP07(2012)177

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