Abstract
If holography is an equivalence between quantum theories, one might expect it to be described by a map that is a bijective isometry between bulk and boundary Hilbert spaces, preserving the hamiltonian and symmetries. Holography has been believed to be a property of gravitational (or string) theories, but not of non-gravitational theories; specifically Marolf has argued that it originates from the gauge symmetries and constraints of gravity. These observations suggest study of the assumed holographic map as a function of the gravitational coupling G. The zero coupling limit gives ordinary quantum field theory, and is therefore not necessarily expected to be holographic. This, and the structure of gravity at non-zero G, raises important questions about the full map. In particular, construction of a holographic map appears to require as input a solution of the nonperturbative analog of the bulk gravitational constraints, that is, the unitary bulk evolution. Moreover, examination of the candidate boundary algebra, including the boundary hamiltonian, reveals commutators that don’t close in the usual fashion expected for a boundary theory.
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References
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].
D. Marolf, Unitarity and holography in gravitational physics, Phys. Rev. D 79 (2009) 044010 [arXiv:0808.2842] [INSPIRE].
D. Marolf, Holographic thought experiments, Phys. Rev. D 79 (2009) 024029 [arXiv:0808.2845] [INSPIRE].
D. Marolf, Holography without strings?, Class. Quant. Grav. 31 (2014) 015008 [arXiv:1308.1977] [INSPIRE].
T. Jacobson, Boundary unitarity and the black hole information paradox, Int. J. Mod. Phys. D 22 (2013) 1342002 [arXiv:1212.6944] [INSPIRE].
T. Jacobson and P. Nguyen, Diffeomorphism invariance and the black hole information paradox, Phys. Rev. D 100 (2019) 046002 [arXiv:1904.04434] [INSPIRE].
S.B. Giddings, Quantum-first gravity, Found. Phys. 49 (2019) 177 [arXiv:1803.04973] [INSPIRE].
S.B. Giddings, Quantum gravity: a quantum-first approach, LHEP 1 (2018) 1 [arXiv:1805.06900] [INSPIRE].
P. Saad, S.H. Shenker and D. Stanford, JT gravity as a matrix integral, arXiv:1903.11115 [INSPIRE].
S.R. Coleman, Black holes as red herrings: topological fluctuations and the loss of quantum coherence, Nucl. Phys. B 307 (1988) 867 [INSPIRE].
S.B. Giddings and A. Strominger, Loss of incoherence and determination of coupling constants in quantum gravity, Nucl. Phys. B 307 (1988) 854 [INSPIRE].
S.B. Giddings and A. Strominger, Baby universes, third quantization and the cosmological constant, Nucl. Phys. B 321 (1989) 481 [INSPIRE].
D. Marolf and H. Maxfield, Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information, JHEP 08 (2020) 044 [arXiv:2002.08950] [INSPIRE].
S.B. Giddings and M. Lippert, Precursors, black holes, and a locality bound, Phys. Rev. D 65 (2002) 024006 [hep-th/0103231] [INSPIRE].
S.B. Giddings and M. Lippert, The information paradox and the locality bound, Phys. Rev. D 69 (2004) 124019 [hep-th/0402073] [INSPIRE].
S.B. Giddings, Locality in quantum gravity and string theory, Phys. Rev. D 74 (2006) 106006 [hep-th/0604072] [INSPIRE].
A. Almheiri, X. Dong and D. Harlow, Bulk locality and quantum error correction in AdS/CFT, JHEP 04 (2015) 163 [arXiv:1411.7041] [INSPIRE].
S.B. Giddings, The gravitational S-matrix: Erice lectures, Subnucl. Ser. 48 (2013) 93 [arXiv:1105.2036] [INSPIRE].
R. Haag, Local quantum physics, fields, particles, algebras, Springer, Berlin (1996).
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].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
X. Dong, D. Harlow and A.C. Wall, Reconstruction of bulk operators within the entanglement wedge in gauge-gravity duality, Phys. Rev. Lett. 117 (2016) 021601 [arXiv:1601.05416] [INSPIRE].
J. Cotler, P. Hayden, G. Penington, G. Salton, B. Swingle and M. Walter, Entanglement wedge reconstruction via universal recovery channels, Phys. Rev. X 9 (2019) 031011 [arXiv:1704.05839] [INSPIRE].
T. Faulkner and A. Lewkowycz, Bulk locality from modular flow, JHEP 07 (2017) 151 [arXiv:1704.05464] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
T. Regge and C. Teitelboim, Role of surface integrals in the Hamiltonian formulation of general relativity, Annals Phys. 88 (1974) 286 [INSPIRE].
S.B. Giddings and A. Kinsella, Gauge-invariant observables, gravitational dressings, and holography in AdS, JHEP 11 (2018) 074 [arXiv:1802.01602] [INSPIRE].
W. Donnelly and S.B. Giddings, Gravitational splitting at first order: quantum information localization in gravity, Phys. Rev. D 98 (2018) 086006 [arXiv:1805.11095] [INSPIRE].
W. Donnelly and S.B. Giddings, Diffeomorphism-invariant observables and their nonlocal algebra, Phys. Rev. D 93 (2016) 024030 [Erratum ibid. 94 (2016) 029903] [arXiv:1507.07921] [INSPIRE].
I. Heemskerk, Construction of bulk fields with gauge redundancy, JHEP 09 (2012) 106 [arXiv:1201.3666] [INSPIRE].
D. Kabat and G. Lifschytz, Decoding the hologram: scalar fields interacting with gravity, Phys. Rev. D 89 (2014) 066010 [arXiv:1311.3020] [INSPIRE].
A. Hamilton, D.N. Kabat, G. Lifschytz and D.A. Lowe, Holographic representation of local bulk operators, Phys. Rev. D 74 (2006) 066009 [hep-th/0606141] [INSPIRE].
I. Heemskerk, D. Marolf, J. Polchinski and J. Sully, Bulk and transhorizon measurements in AdS/CFT, JHEP 10 (2012) 165 [arXiv:1201.3664] [INSPIRE].
M. Henneaux and C. Teitelboim, Asymptotically Anti-de Sitter spaces, Commun. Math. Phys. 98 (1985) 391 [INSPIRE].
W. Donnelly and S.B. Giddings, How is quantum information localized in gravity?, Phys. Rev. D 96 (2017) 086013 [arXiv:1706.03104] [INSPIRE].
D.L. Jafferis, A. Lewkowycz, J. Maldacena and S.J. Suh, Relative entropy equals bulk relative entropy, JHEP 06 (2016) 004 [arXiv:1512.06431] [INSPIRE].
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Giddings, S.B. Holography and unitarity. J. High Energ. Phys. 2020, 56 (2020). https://doi.org/10.1007/JHEP11(2020)056
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DOI: https://doi.org/10.1007/JHEP11(2020)056