Menagerie of AdS2 boundary conditions

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

We consider different sets of AdS2 boundary conditions for the Jackiw-Teitelboim model in the linear dilaton sector where the dilaton is allowed to fluctuate to leading order at the boundary of the Poincaré disk. The most general set of boundary conditions is easily motivated in the gauge theoretic formulation as a Poisson sigma model and has an \( \mathfrak{s}\mathfrak{l}(2) \) current algebra as asymptotic symmetries. Consistency of the variational principle requires a novel boundary counterterm in the holographically renormalized action, namely a kinetic term for the dilaton. The on-shell action can be naturally reformulated as a Schwarzian boundary action. While there can be at most three canonical boundary charges on an equal-time slice, we consider all Fourier modes of these charges with respect to the Euclidean boundary time and study their associated algebras. Besides the (centerless) \( \mathfrak{s}\mathfrak{l}(2) \) current algebra we find for stricter boundary conditions a Virasoro algebra, a warped conformal algebra and a \( \mathfrak{u}(1) \) current algebra. In each of these cases we get one half of a corresponding symmetry algebra in three-dimensional Einstein gravity with negative cosmological constant and analogous boundary conditions. However, on-shell some of these algebras reduce to finite-dimensional ones, reminiscent of the on-shell breaking of conformal invariance in SYK. We conclude with a discussion of thermodynamical aspects, in particular the entropy and some Cardyology.

A preprint version of the article is available at ArXiv.

References

  1. [1]

    R. Jackiw, Liouville field theory: a two-dimensional model for gravity?, in Quantum theory of gravity, S. Christensen ed., Adam Hilger, Bristol U.K., (1984), pg. 403.

  2. [2]

    C. Teitelboim, The Hamiltonian structure of two-dimensional space-time and its relation with the conformal anomaly, in Quantum theory of gravity, S. Christensen ed., Adam Hilger, Bristol U.K., (1984), pg. 327.

  3. [3]

    G. Mandal, A.M. Sengupta and S.R. Wadia, Classical solutions of two-dimensional string theory, Mod. Phys. Lett. A 6 (1991) 1685 [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  4. [4]

    S. Elitzur, A. Forge and E. Rabinovici, Some global aspects of string compactifications, Nucl. Phys. B 359 (1991) 581 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  5. [5]

    E. Witten, On string theory and black holes, Phys. Rev. D 44 (1991) 314 [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  6. [6]

    R. Dijkgraaf, H.L. Verlinde and E.P. Verlinde, String propagation in a black hole geometry, Nucl. Phys. B 371 (1992) 269 [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  7. [7]

    C.G. Callan Jr., S.B. Giddings, J.A. Harvey and A. Strominger, Evanescent black holes, Phys. Rev. D 45 (1992) R1005 [hep-th/9111056] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  8. [8]

    S.D. Odintsov and I.L. Shapiro, One loop renormalization of two-dimensional induced quantum gravity, Phys. Lett. B 263 (1991) 183 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  9. [9]

    J.G. Russo and A.A. Tseytlin, Scalar tensor quantum gravity in two-dimensions, Nucl. Phys. B 382 (1992) 259 [hep-th/9201021] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  10. [10]

    W. Kummer, H. Liebl and D.V. Vassilevich, Exact path integral quantization of generic 2D dilaton gravity, Nucl. Phys. B 493 (1997) 491 [gr-qc/9612012] [INSPIRE].

  11. [11]

    J. Brown, Lower dimensional gravity, World Scientific, Singapore, (1988) [INSPIRE].

  12. [12]

    D. Grumiller, W. Kummer and D.V. Vassilevich, Dilaton gravity in two-dimensions, Phys. Rept. 369 (2002) 327 [hep-th/0204253] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  13. [13]

    D. Grumiller and R. Meyer, Ramifications of lineland, Turk. J. Phys. 30 (2006) 349 [hep-th/0604049] [INSPIRE].

    Google Scholar 

  14. [14]

    J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].

    MathSciNet  Article  MATH  Google Scholar 

  15. [15]

    S.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].

    ADS  Article  MATH  Google Scholar 

  16. [16]

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

    ADS  MathSciNet  Article  MATH  Google Scholar 

  17. [17]

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

    ADS  MathSciNet  Article  MATH  Google Scholar 

  18. [18]

    R. Emparan, C.V. Johnson and R.C. Myers, Surface terms as counterterms in the AdS/CFT correspondence, Phys. Rev. D 60 (1999) 104001 [hep-th/9903238] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  19. [19]

    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].

    ADS  Article  MATH  Google Scholar 

  20. [20]

    I. Papadimitriou and K. Skenderis, AdS/CFT correspondence and geometry, IRMA Lect. Math. Theor. Phys. 8 (2005) 73 [hep-th/0404176] [INSPIRE].

    MathSciNet  MATH  Google Scholar 

  21. [21]

    J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].

    ADS  Google Scholar 

  22. [22]

    A. Kitaev, A simple model of quantum holography (part 1), in KITP strings seminars, http://online.kitp.ucsb.edu/online/entangled15/kitaev/, Kavli Institute for Theoretical Physics, University of California, Santa Barbara U.S.A., 7 April 2015.

  23. [23]

    A. Kitaev, A simple model of quantum holography (part 2), in KITP strings seminars, http://online.kitp.ucsb.edu/online/entangled15/kitaev2/, Kavli Institute for Theoretical Physics, University of California, Santa Barbara U.S.A., 27 May 2015.

  24. [24]

    S. Sachdev and J. Ye, Gapless spin fluid ground state in a random, quantum Heisenberg magnet, Phys. Rev. Lett. 70 (1993) 3339 [cond-mat/9212030] [INSPIRE].

  25. [25]

    S. Sachdev, Holographic metals and the fractionalized Fermi liquid, Phys. Rev. Lett. 105 (2010) 151602 [arXiv:1006.3794] [INSPIRE].

    ADS  Article  Google Scholar 

  26. [26]

    J. Polchinski and V. Rosenhaus, The spectrum in the Sachdev-Ye-Kitaev model, JHEP 04 (2016) 001 [arXiv:1601.06768] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  27. [27]

    Y.-Z. You, A.W.W. Ludwig and C. Xu, Sachdev-Ye-Kitaev model and thermalization on the boundary of many-body localized fermionic symmetry protected topological states, Phys. Rev. B 95 (2017) 115150 [arXiv:1602.06964] [INSPIRE].

    ADS  Article  Google Scholar 

  28. [28]

    A. Jevicki, K. Suzuki and J. Yoon, Bi-local holography in the SYK model, JHEP 07 (2016) 007 [arXiv:1603.06246] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  29. [29]

    K. Jensen, Chaos in AdS 2 holography, Phys. Rev. Lett. 117 (2016) 111601 [arXiv:1605.06098] [INSPIRE].

    ADS  Article  Google Scholar 

  30. [30]

    J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional nearly anti-de-Sitter space, Prog. Theor. Exp. Phys. 2016 (2016) 12C104 [arXiv:1606.01857] [INSPIRE].

  31. [31]

    J. Engelsöy, T.G. Mertens and H. Verlinde, An investigation of AdS 2 backreaction and holography, JHEP 07 (2016) 139 [arXiv:1606.03438] [INSPIRE].

    ADS  Article  Google Scholar 

  32. [32]

    D. Bagrets, A. Altland and A. Kamenev, Sachdev-Ye-Kitaev model as Liouville quantum mechanics, Nucl. Phys. B 911 (2016) 191 [arXiv:1607.00694] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  33. [33]

    L. García- Álvarez, I.L. Egusquiza, L. Lamata, A. del Campo, J. Sonner and E. Solano, Digital quantum simulation of minimal AdS/CFT, Phys. Rev. Lett. 119 (2017) 040501 [arXiv:1607.08560] [INSPIRE].

  34. [34]

    A. Jevicki and K. Suzuki, Bi-local holography in the SYK model: perturbations, JHEP 11 (2016) 046 [arXiv:1608.07567] [INSPIRE].

    MathSciNet  Article  Google Scholar 

  35. [35]

    Y. Gu, X.-L. Qi and D. Stanford, Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models, JHEP 05 (2017) 125 [arXiv:1609.07832] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  36. [36]

    D.J. Gross and V. Rosenhaus, A generalization of Sachdev-Ye-Kitaev, JHEP 02 (2017) 093 [arXiv:1610.01569] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  37. [37]

    M. Berkooz, P. Narayan, M. Rozali and J. Simón, Higher dimensional generalizations of the SYK model, JHEP 01 (2017) 138 [arXiv:1610.02422] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  38. [38]

    A.M. García-García and J.J.M. Verbaarschot, Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 126010 [arXiv:1610.03816] [INSPIRE].

    ADS  Google Scholar 

  39. [39]

    S. Banerjee and E. Altman, Solvable model for a dynamical quantum phase transition from fast to slow scrambling, Phys. Rev. B 95 (2017) 134302 [arXiv:1610.04619] [INSPIRE].

    ADS  Article  Google Scholar 

  40. [40]

    W. Fu, D. Gaiotto, J. Maldacena and S. Sachdev, Supersymmetric Sachdev-Ye-Kitaev models, Phys. Rev. D 95 (2017) 026009 [Addendum ibid. D 95 (2017) 069904] [arXiv:1610.08917] [INSPIRE].

  41. [41]

    E. Witten, An SYK-like model without disorder, arXiv:1610.09758 [INSPIRE].

  42. [42]

    J.S. Cotler et al., Black holes and random matrices, JHEP 05 (2017) 118 [arXiv:1611.04650] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  43. [43]

    I.R. Klebanov and G. Tarnopolsky, Uncolored random tensors, melon diagrams and the Sachdev-Ye-Kitaev models, Phys. Rev. D 95 (2017) 046004 [arXiv:1611.08915] [INSPIRE].

  44. [44]

    R.A. Davison, W. Fu, A. Georges, Y. Gu, K. Jensen and S. Sachdev, Thermoelectric transport in disordered metals without quasiparticles: the Sachdev-Ye-Kitaev models and holography, Phys. Rev. B 95 (2017) 155131 [arXiv:1612.00849] [INSPIRE].

    ADS  Article  Google Scholar 

  45. [45]

    C. Peng, M. Spradlin and A. Volovich, A supersymmetric SYK-like tensor model, JHEP 05 (2017) 062 [arXiv:1612.03851] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  46. [46]

    C. Krishnan, S. Sanyal and P.N. Bala Subramanian, Quantum chaos and holographic tensor models, JHEP 03 (2017) 056 [arXiv:1612.06330] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  47. [47]

    G. Turiaci and H. Verlinde, Towards a 2d QFT analog of the SYK model, arXiv:1701.00528 [INSPIRE].

  48. [48]

    F. Ferrari, The large D limit of planar diagrams, arXiv:1701.01171 [INSPIRE].

  49. [49]

    Z. Bi, C.-M. Jian, Y.-Z. You, K.A. Pawlak and C. Xu, Instability of the non-Fermi liquid state of the Sachdev-Ye-Kitaev model, Phys. Rev. B 95 (2017) 205105 [arXiv:1701.07081] [INSPIRE].

    ADS  Article  Google Scholar 

  50. [50]

    T. Li, J. Liu, Y. Xin and Y. Zhou, Supersymmetric SYK model and random matrix theory, JHEP 06 (2017) 111 [arXiv:1702.01738] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  51. [51]

    R. Gurau, Quenched equals annealed at leading order in the colored SYK model, arXiv:1702.04228 [INSPIRE].

  52. [52]

    G. Mandal, P. Nayak and S.R. Wadia, Coadjoint orbit action of Virasoro group and two-dimensional quantum gravity dual to SYK/tensor models, arXiv:1702.04266 [INSPIRE].

  53. [53]

    D.J. Gross and V. Rosenhaus, The bulk dual of SYK: cubic couplings, JHEP 05 (2017) 092 [arXiv:1702.08016] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  54. [54]

    T.G. Mertens, G.J. Turiaci and H.L. Verlinde, Solving the Schwarzian via the conformal bootstrap, JHEP 08 (2017) 136 [arXiv:1705.08408] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  55. [55]

    C. Krishnan and K.V.P. Kumar, Towards a finite-N hologram, JHEP 10 (2017) 099 [arXiv:1706.05364] [INSPIRE].

    ADS  Article  Google Scholar 

  56. [56]

    H.K. Kunduri, J. Lucietti and H.S. Reall, Near-horizon symmetries of extremal black holes, Class. Quant. Grav. 24 (2007) 4169 [arXiv:0705.4214] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  57. [57]

    A. Strominger, AdS 2 quantum gravity and string theory, JHEP 01 (1999) 007 [hep-th/9809027] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  58. [58]

    J.M. Maldacena, J. Michelson and A. Strominger, Anti-de Sitter fragmentation, JHEP 02 (1999) 011 [hep-th/9812073] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  59. [59]

    M. Brigante, S. Cacciatori, D. Klemm and D. Zanon, The asymptotic dynamics of two-dimensional (anti-)de Sitter gravity, JHEP 03 (2002) 005 [hep-th/0202073] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  60. [60]

    M. Astorino, S. Cacciatori, D. Klemm and D. Zanon, AdS 2 supergravity and superconformal quantum mechanics, Annals Phys. 304 (2003) 128 [hep-th/0212096] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  61. [61]

    H.L. Verlinde, Superstrings on AdS 2 and superconformal matrix quantum mechanics, hep-th/0403024 [INSPIRE].

  62. [62]

    R.K. Gupta and A. Sen, AdS 3 /CFT 2 to AdS 2 /CFT 1, JHEP 04 (2009) 034 [arXiv:0806.0053] [INSPIRE].

    ADS  Article  Google Scholar 

  63. [63]

    M. Alishahiha and F. Ardalan, Central charge for 2D gravity on AdS 2 and AdS 2 /CFT 1 correspondence, JHEP 08 (2008) 079 [arXiv:0805.1861] [INSPIRE].

    ADS  Article  Google Scholar 

  64. [64]

    A. Sen, Quantum entropy function from AdS 2 /CFT 1 correspondence, Int. J. Mod. Phys. A 24 (2009) 4225 [arXiv:0809.3304] [INSPIRE].

  65. [65]

    T. Hartman and A. Strominger, Central charge for AdS 2 quantum gravity, JHEP 04 (2009) 026 [arXiv:0803.3621] [INSPIRE].

    ADS  Article  Google Scholar 

  66. [66]

    A. Castro, D. Grumiller, F. Larsen and R. McNees, Holographic description of AdS 2 black holes, JHEP 11 (2008) 052 [arXiv:0809.4264] [INSPIRE].

    ADS  Article  Google Scholar 

  67. [67]

    V. Balasubramanian, J. de Boer, M.M. Sheikh-Jabbari and J. Simón, What is a chiral 2d CFT? And what does it have to do with extremal black holes?, JHEP 02 (2010) 017 [arXiv:0906.3272] [INSPIRE].

  68. [68]

    A. Castro and F. Larsen, Near extremal Kerr entropy from AdS 2 quantum gravity, JHEP 12 (2009) 037 [arXiv:0908.1121] [INSPIRE].

    ADS  Article  Google Scholar 

  69. [69]

    D. Grumiller, J. Salzer and D. Vassilevich, AdS 2 holography is (non-)trivial for (non-)constant dilaton, JHEP 12 (2015) 015 [arXiv:1509.08486] [INSPIRE].

    ADS  Google Scholar 

  70. [70]

    D. Grumiller and R. McNees, Thermodynamics of black holes in two (and higher) dimensions, JHEP 04 (2007) 074 [hep-th/0703230] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  71. [71]

    M. Cvetič and I. Papadimitriou, AdS 2 holographic dictionary, JHEP 12 (2016) 008 [Erratum ibid. 01 (2017) 120] [arXiv:1608.07018] [INSPIRE].

  72. [72]

    D. Grumiller, M. Leston and D. Vassilevich, Anti-de Sitter holography for gravity and higher spin theories in two dimensions, Phys. Rev. D 89 (2014) 044001 [arXiv:1311.7413] [INSPIRE].

  73. [73]

    D. Grumiller, R. McNees and J. Salzer, Cosmological constant as confining U(1) charge in two-dimensional dilaton gravity, Phys. Rev. D 90 (2014) 044032 [arXiv:1406.7007] [INSPIRE].

  74. [74]

    W. Kummer, H. Liebl and D.V. Vassilevich, Integrating geometry in general 2D dilaton gravity with matter, Nucl. Phys. B 544 (1999) 403 [hep-th/9809168] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  75. [75]

    W. Kummer and D.V. Vassilevich, Hawking radiation from dilaton gravity in (1 + 1)-dimensions: a pedagogical review, Annalen Phys. 8 (1999) 801 [gr-qc/9907041] [INSPIRE].

  76. [76]

    D. Grumiller, W. Kummer and D.V. Vassilevich, The virtual black hole in 2D quantum gravity, Nucl. Phys. B 580 (2000) 438 [gr-qc/0001038] [INSPIRE].

  77. [77]

    P. Fischer, D. Grumiller, W. Kummer and D.V. Vassilevich, S-matrix for s-wave gravitational scattering, Phys. Lett. B 521 (2001) 357 [Erratum ibid. B 532 (2002) 373] [gr-qc/0105034] [INSPIRE].

  78. [78]

    A. Almheiri and J. Polchinski, Models of AdS 2 backreaction and holography, JHEP 11 (2015) 014 [arXiv:1402.6334] [INSPIRE].

    ADS  Article  Google Scholar 

  79. [79]

    D. Grumiller and M. Riegler, Most general AdS 3 boundary conditions, JHEP 10 (2016) 023 [arXiv:1608.01308] [INSPIRE].

    ADS  Article  Google Scholar 

  80. [80]

    S.W. Hawking, M.J. Perry and A. Strominger, Soft hair on black holes, Phys. Rev. Lett. 116 (2016) 231301 [arXiv:1601.00921] [INSPIRE].

    ADS  Article  Google Scholar 

  81. [81]

    L. Donnay, G. Giribet, H.A. Gonzalez and M. Pino, Supertranslations and superrotations at the black hole horizon, Phys. Rev. Lett. 116 (2016) 091101 [arXiv:1511.08687] [INSPIRE].

  82. [82]

    H. Afshar et al., Soft Heisenberg hair on black holes in three dimensions, Phys. Rev. D 93 (2016) 101503 [arXiv:1603.04824] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  83. [83]

    M. Cadoni and S. Mignemi, Asymptotic symmetries of AdS 2 and conformal group in D = 1, Nucl. Phys. B 557 (1999) 165 [hep-th/9902040] [INSPIRE].

  84. [84]

    V. de Alfaro, S. Fubini and G. Furlan, Conformal invariance in quantum mechanics, Nuovo Cim. A 34 (1976) 569 [INSPIRE].

    ADS  Article  Google Scholar 

  85. [85]

    V.G. Knizhnik, A.M. Polyakov and A.B. Zamolodchikov, Fractal structure of 2D quantum gravity, Mod. Phys. Lett. A 3 (1988) 819 [INSPIRE].

  86. [86]

    F. David, Conformal field theories coupled to 2D gravity in the conformal gauge, Mod. Phys. Lett. A 3 (1988) 1651 [INSPIRE].

    ADS  Article  Google Scholar 

  87. [87]

    J. Distler and H. Kawai, Conformal field theory and 2D quantum gravity, Nucl. Phys. B 321 (1989) 509 [INSPIRE].

  88. [88]

    D. Grumiller, J. Salzer and D. Vassilevich, Aspects of AdS 2 holography with non-constant dilaton, Russ. Phys. J. 59 (2017) 1798 [arXiv:1607.06974] [INSPIRE].

  89. [89]

    A. Achucarro and P.K. Townsend, A Chern-Simons action for three-dimensional anti-de Sitter supergravity theories, Phys. Lett. B 180 (1986) 89 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  90. [90]

    E. Witten, (2 + 1)-dimensional gravity as an exactly soluble system, Nucl. Phys. B 311 (1988) 46 [INSPIRE].

  91. [91]

    P. Schaller and T. Strobl, Poisson structure induced (topological) field theories, Mod. Phys. Lett. A 9 (1994) 3129 [hep-th/9405110] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  92. [92]

    N. Ikeda, Two-dimensional gravity and nonlinear gauge theory, Annals Phys. 235 (1994) 435 [hep-th/9312059] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  93. [93]

    D.V. Vassilevich, Holographic duals to Poisson σ-models and noncommutative quantum mechanics, Phys. Rev. D 87 (2013) 104011 [arXiv:1301.7029] [INSPIRE].

    ADS  Google Scholar 

  94. [94]

    G. Barnich and C. Troessaert, Aspects of the BMS/CFT correspondence, JHEP 05 (2010) 062 [arXiv:1001.1541] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  95. [95]

    E. Witten, Coadjoint orbits of the Virasoro group, Commun. Math. Phys. 114 (1988) 1 [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  96. [96]

    B. Oblak, BMS particles in three dimensions, arXiv:1610.08526 [INSPIRE].

  97. [97]

    T.H. Buscher, A symmetry of the string background field equations, Phys. Lett. B 194 (1987) 59 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  98. [98]

    T.H. Buscher, Path integral derivation of quantum duality in nonlinear σ-models, Phys. Lett. B 201 (1988) 466 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  99. [99]

    R.M. Wald and A. Zoupas, A general definition of ‘conserved quantities’ in general relativity and other theories of gravity, Phys. Rev. D 61 (2000) 084027 [gr-qc/9911095] [INSPIRE].

  100. [100]

    G. Barnich and F. Brandt, Covariant theory of asymptotic symmetries, conservation laws and central charges, Nucl. Phys. B 633 (2002) 3 [hep-th/0111246] [INSPIRE].

  101. [101]

    T. Regge and C. Teitelboim, Role of surface integrals in the Hamiltonian formulation of general relativity, Annals Phys. 88 (1974) 286 [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  102. [102]

    M. Cadoni and S. Mignemi, Symmetry breaking, central charges and the AdS 2 /CFT 1 correspondence, Phys. Lett. B 490 (2000) 131 [hep-th/0002256] [INSPIRE].

    ADS  Article  Google Scholar 

  103. [103]

    G. Barnich and C. Troessaert, BMS charge algebra, JHEP 12 (2011) 105 [arXiv:1106.0213] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  104. [104]

    S. Detournay, T. Hartman and D.M. Hofman, Warped conformal field theory, Phys. Rev. D 86 (2012) 124018 [arXiv:1210.0539] [INSPIRE].

    ADS  Google Scholar 

  105. [105]

    H. Afshar, S. Detournay, D. Grumiller and B. Oblak, Near-horizon geometry and warped conformal symmetry, JHEP 03 (2016) 187 [arXiv:1512.08233] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  106. [106]

    C. Troessaert, Enhanced asymptotic symmetry algebra of AdS 3, JHEP 08 (2013) 044 [arXiv:1303.3296] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  107. [107]

    H. Afshar, D. Grumiller, W. Merbis, A. Perez, D. Tempo and R. Troncoso, Soft hairy horizons in three spacetime dimensions, Phys. Rev. D 95 (2017) 106005 [arXiv:1611.09783] [INSPIRE].

    ADS  Google Scholar 

  108. [108]

    J. Gegenberg, G. Kunstatter and D. Louis-Martinez, Observables for two-dimensional black holes, Phys. Rev. D 51 (1995) 1781 [gr-qc/9408015] [INSPIRE].

  109. [109]

    G. Barnich, H.A. González and P. Salgado-Rebolledo, Geometric actions for three-dimensional gravity, arXiv:1707.08887 [INSPIRE].

  110. [110]

    A. Bagchi, D. Grumiller, J. Salzer, S. Sarkar and F. Schöller, Flat space cosmologies in two dimensions: phase transitions and asymptotic mass-domination, Phys. Rev. D 90 (2014) 084041 [arXiv:1408.5337] [INSPIRE].

    ADS  Google Scholar 

  111. [111]

    G. Compère, P. Mao, A. Seraj and M.M. Sheikh-Jabbari, Symplectic and Killing symmetries of AdS 3 gravity: holographic vs boundary gravitons, JHEP 01 (2016) 080 [arXiv:1511.06079] [INSPIRE].

    ADS  Article  Google Scholar 

  112. [112]

    T. Strobl, Gravity in two space-time dimensions, hep-th/0011240 [INSPIRE].

Download references

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.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Daniel Grumiller.

Additional information

ArXiv ePrint: 1708.08471

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Grumiller, D., McNees, R., Salzer, J. et al. Menagerie of AdS2 boundary conditions. J. High Energ. Phys. 2017, 203 (2017). https://doi.org/10.1007/JHEP10(2017)203

Download citation

Keywords

  • 2D Gravity
  • AdS-CFT Correspondence
  • Topological Field Theories