Journal of High Energy Physics

, 2019:25 | Cite as

Holographic BCFT with Dirichlet boundary condition

  • Rong-Xin MiaoEmail author
Open Access
Regular Article - Theoretical Physics


Neumann boundary condition plays an important role in the initial proposal of holographic dual of boundary conformal field theory, which has yield many interesting results and passed several non-trivial tests. In this paper, we show that Dirichlet boundary condition works as well as Neumann boundary condition. For instance, it includes AdS solution and obeys the g-theorem. Furthermore, it can produce the correct expression of one point function, the boundary Weyl anomaly and the universal relations between them. We also study the relative boundary condition for gauge fields, which is the counterpart of Dirichlet boundary condition for gravitational fields. Interestingly, the four-dimensional Reissner-Nordström black hole with magnetic charge is an exact solution to relative boundary condition under some conditions. This holographic model predicts that a constant magnetic field in the bulk can induce a constant current on the boundary in three dimensions. We suggest to measure this interesting boundary current in materials such as the graphene.


AdS-CFT Correspondence Classical Theories of Gravity 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


  1. [1]
    J.L. Cardy, Boundary conformal field theory, hep-th/0411189 [INSPIRE].
  2. [2]
    D.M. McAvity and H. Osborn, Energy momentum tensor in conformal field theories near a boundary, Nucl. Phys. B 406 (1993) 655 [hep-th/9302068] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    D. Fursaev, Conformal anomalies of CFT’s with boundaries, JHEP 12 (2015) 112 [arXiv:1510.01427] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  4. [4]
    C.P. Herzog, K.-W. Huang and K. Jensen, Universal Entanglement and Boundary Geometry in Conformal Field Theory, JHEP 01 (2016) 162 [arXiv:1510.00021] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    R.-X. Miao and C.-S. Chu, Universality for Shape Dependence of Casimir Effects from Weyl Anomaly, JHEP 03 (2018) 046 [arXiv:1706.09652] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    C. Herzog, K.-W. Huang and K. Jensen, Displacement Operators and Constraints on Boundary Central Charges, Phys. Rev. Lett. 120 (2018) 021601 [arXiv:1709.07431] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    K. Jensen, E. Shaverin and A. Yarom, ’t Hooft anomalies and boundaries, JHEP 01 (2018) 085 [arXiv:1710.07299] [INSPIRE].
  8. [8]
    M. Kurkov and D. Vassilevich, Parity anomaly in four dimensions, Phys. Rev. D 96 (2017) 025011 [arXiv:1704.06736] [INSPIRE].ADSMathSciNetGoogle Scholar
  9. [9]
    M. Kurkov and D. Vassilevich, Gravitational parity anomaly with and without boundaries, JHEP 03 (2018) 072 [arXiv:1801.02049] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    D. Vassilevich, Index Theorems and Domain Walls, JHEP 07 (2018) 108 [arXiv:1805.09974] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    D. Rodriguez-Gomez and J.G. Russo, Free energy and boundary anomalies on \( \mathbb{S} \) a × ℍb spaces, JHEP 10 (2017) 084 [arXiv:1708.00305] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    D. Seminara, J. Sisti and E. Tonni, Corner contributions to holographic entanglement entropy in AdS 4 /BCFT 3, JHEP 11 (2017) 076 [arXiv:1708.05080] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  13. [13]
    J. Erdmenger, M. Flory, C. Hoyos, M.-N. Newrzella and J.M.S. Wu, Entanglement Entropy in a Holographic Kondo Model, Fortsch. Phys. 64 (2016) 109 [arXiv:1511.03666] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    J. Erdmenger, M. Flory and M.-N. Newrzella, Bending branes for DCFT in two dimensions, JHEP 01 (2015) 058 [arXiv:1410.7811] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  15. [15]
    M. Flory, A complexity/fidelity susceptibility g-theorem for AdS 3 /BCFT 2, JHEP 06 (2017) 131 [arXiv:1702.06386] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    C.-S. Chu and R.-X. Miao, Weyl Anomaly Induced Current in Boundary Quantum Field Theories, Phys. Rev. Lett. 121 (2018) 251602 [arXiv:1803.03068] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    C.-S. Chu and R.-X. Miao, Anomalous Transport in Holographic Boundary Conformal Field Theories, JHEP 07 (2018) 005 [arXiv:1804.01648] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    R.-X. Miao, Casimir Effect, Weyl Anomaly and Displacement Operator in Boundary Conformal Field Theory, arXiv:1808.05783 [INSPIRE].
  19. [19]
    C.-S. Chu and R.-X. Miao, Boundary String Current & Weyl Anomaly in Six-dimensional Conformal Field Theory, arXiv:1812.10273 [INSPIRE].
  20. [20]
    J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    T. Takayanagi, Holographic Dual of BCFT, Phys. Rev. Lett. 107 (2011) 101602 [arXiv:1105.5165] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    M. Nozaki, T. Takayanagi and T. Ugajin, Central Charges for BCFTs and Holography, JHEP 06 (2012) 066 [arXiv:1205.1573] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    M. Fujita, T. Takayanagi and E. Tonni, Aspects of AdS/BCFT, JHEP 11 (2011) 043 [arXiv:1108.5152] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    D.M. McAvity and H. Osborn, A DeWitt expansion of the heat kernel for manifolds with a boundary, Class. Quant. Grav. 8 (1991) 603 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    C.P. Herzog and K.-W. Huang, Boundary Conformal Field Theory and a Boundary Central Charge, JHEP 10 (2017) 189 [arXiv:1707.06224] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    G.W. Gibbons and S.W. Hawking, Action Integrals and Partition Functions in Quantum Gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].ADSGoogle Scholar
  27. [27]
    J.W. York Jr., Role of conformal three geometry in the dynamics of gravitation, Phys. Rev. Lett. 28 (1972) 1082 [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    M.T. Anderson, On quasi-local Hamiltonians in General Relativity, Phys. Rev. D 82 (2010) 084044 [arXiv:1008.4309] [INSPIRE].ADSGoogle Scholar
  29. [29]
    E. Witten, A Note On Boundary Conditions In Euclidean Gravity, arXiv:1805.11559 [INSPIRE].
  30. [30]
    R.-X. Miao, C.-S. Chu and W.-Z. Guo, New proposal for a holographic boundary conformal field theory, Phys. Rev. D 96 (2017) 046005 [arXiv:1701.04275] [INSPIRE].ADSMathSciNetGoogle Scholar
  31. [31]
    C.-S. Chu, R.-X. Miao and W.-Z. Guo, On New Proposal for Holographic BCFT, JHEP 04 (2017) 089 [arXiv:1701.07202] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    A. Lewkowycz and E. Perlmutter, Universality in the geometric dependence of Renyi entropy, JHEP 01 (2015) 080 [arXiv:1407.8171] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  33. [33]
    X. Dong, Shape Dependence of Holographic Rényi Entropy in Conformal Field Theories, Phys. Rev. Lett. 116 (2016) 251602 [arXiv:1602.08493] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  34. [34]
    E.-J. Chang, C.-J. Chou and Y. Yang, Holographic entanglement entropy in boundary conformal field theory, Phys. Rev. D 98 (2018) 106016 [arXiv:1805.06117] [INSPIRE].ADSGoogle Scholar
  35. [35]
    M.A.H. Vozmediano, M.I. Katsnelson and F. Guinea, Gauge fields in graphene, Phys. Rept. 496 (2010) 109 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  36. [36]
    F. de Juan, M. Sturla and M.A.H. Vozmediano, Space dependent Fermi velocity in strained graphene, Phys. Rev. Lett. 108 (2012) 227205 [arXiv:1201.2656] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    J. Scott Bunch et al., Impermeable Atomic Membranes from Graphene Sheets, Nano Lett. 8 (2008) 2458.ADSCrossRefGoogle Scholar
  38. [38]
    G.E. Volovik and M.A. Zubkov, Emergent Hořava gravity in graphene, Annals Phys. 340 (2014) 352 [arXiv:1305.4665] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    A. Faraji Astaneh and S.N. Solodukhin, Holographic calculation of boundary terms in conformal anomaly, Phys. Lett. B 769 (2017) 25 [arXiv:1702.00566] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  40. [40]
    S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  41. [41]
    D. Deutsch and P. Candelas, Boundary Effects in Quantum Field Theory, Phys. Rev. D 20 (1979) 3063 [INSPIRE].ADSMathSciNetGoogle Scholar
  42. [42]
    K. Jensen and A. O’Bannon, Constraint on Defect and Boundary Renormalization Group Flows, Phys. Rev. Lett. 116 (2016) 091601 [arXiv:1509.02160] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    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].ADSCrossRefzbMATHGoogle Scholar
  44. [44]
    A. Buchel, J. Escobedo, R.C. Myers, M.F. Paulos, A. Sinha and M. Smolkin, Holographic GB gravity in arbitrary dimensions, JHEP 03 (2010) 111 [arXiv:0911.4257] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.School of Physics and AstronomySun Yat-Sen UniversityZhuhaiChina

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