Entanglement dynamics in 2D CFT with boundary: entropic origin of JT gravity and Schwarzian QM. (English) Zbl 1416.83072
Summary: We study the dynamics of the geometric entanglement entropy of a 2D CFT in the presence of a boundary. We show that this dynamics is governed by local equations of motion, that take the same form as 2D Jackiw-Teitelboim gravity coupled to the CFT. If we assume that the boundary has a small thickness \( \epsilon \) and constant boundary entropy, we derive that its location satisfies the equations of motion of Schwarzian quantum mechanics with coupling constant \( C = c \epsilon /12 \pi \). We rederive this result via energy-momentum conservation.
MSC:
| 83C80 | Analogues of general relativity in lower dimensions |
| 81P40 | Quantum coherence, entanglement, quantum correlations |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |
| 81S10 | Geometry and quantization, symplectic methods |
Keywords:
2D gravity; 2D Jackiw-Teitelboim gravity; conformal field theory; field theories in lower dimensions; ArXiv ePrint: 1808.05583References:
| [1] | T. Jacobson, Thermodynamics of space-time: the Einstein equation of state, Phys. Rev. Lett.75 (1995) 1260 [gr-qc/9504004] [INSPIRE]. · Zbl 1020.83609 |
| [2] | R. Bousso, Z. Fisher, S. Leichenauer and A.C. Wall, Quantum focusing conjecture, Phys. Rev.D 93 (2016) 064044 [arXiv:1506.02669] [INSPIRE]. |
| [3] | S. Balakrishnan, T. Faulkner, Z.U. Khandker and H. Wang, A general proof of the quantum null energy condition, arXiv:1706.09432 [INSPIRE]. · Zbl 1423.81149 |
| [4] | S. Leichenauer, A. Levine and A. Shahbazi-Moghaddam, Energy density from second shape variations of the von Neumann entropy, Phys. Rev.D 98 (2018) 086013 [arXiv:1802.02584] [INSPIRE]. |
| [5] | J. Koeller, S. Leichenauer, A. Levine and A. Shahbazi-Moghaddam, Local modular hamiltonians from the quantum null energy condition, Phys. Rev.D 97 (2018) 065011 [arXiv:1702.00412] [INSPIRE]. |
| [6] | R. Jackiw, Lower dimensional gravity, Nucl. Phys.B 252 (1985) 343 [INSPIRE]. |
| [7] | C. Teitelboim, Gravitation and hamiltonian structure in two space-time dimensions, Phys. Lett.B 126 (1983) 41. |
| [8] | J. Engelsöy, T.G. Mertens and H. Verlinde, An investigation of AdS2backreaction and holography, JHEP07 (2016) 139 [arXiv:1606.03438] [INSPIRE]. · Zbl 1390.83104 |
| [9] | A. Kitaev, Hidden correlations in the Hawking radiation and thermal noise, talk given at the Fundamental Physics Prize Symposium, November 10, Stanford University, Stanford, U.S.A. (2014). |
| [10] | A. Kitaev, Hidden correlations in the Hawking radiation and thermal noise, talk given at KITP, February 12, Santa Barbara, U.S.A. (2015). |
| [11] | A. Kitaev, A simple model of quantum holography, talks given at KITP, April 7 and May 27, Santa Barbara, U.S.A. (2015). |
| [12] | J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev.D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE]. |
| [13] | K. Jensen, Chaos in AdS2holography, Phys. Rev. Lett.117 (2016) 111601 [arXiv:1605.06098] [INSPIRE]. |
| [14] | J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional nearly Anti-de-Sitter space, PTEP2016 (2016) 12C104 [arXiv:1606.01857] [INSPIRE]. · Zbl 1361.81112 |
| [15] | C. Holzhey, F. Larsen and F. Wilczek, Geometric and renormalized entropy in conformal field theory, Nucl. Phys.B 424 (1994) 443 [hep-th/9403108] [INSPIRE]. · Zbl 0990.81564 |
| [16] | J. Cardy and E. Tonni, Entanglement hamiltonians in two-dimensional conformal field theory, J. Stat. Mech.1612 (2016) 123103 [arXiv:1608.01283] [INSPIRE]. · Zbl 1456.81364 · doi:10.1088/1742-5468/2016/12/123103 |
| [17] | J. de Boer, F.M. Haehl, M.P. Heller and R.C. Myers, Entanglement, holography and causal diamonds, JHEP08 (2016) 162 [arXiv:1606.03307] [INSPIRE]. · Zbl 1390.83135 · doi:10.1007/JHEP08(2016)162 |
| [18] | H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP05 (2011) 036 [arXiv:1102.0440] [INSPIRE]. · Zbl 1296.81073 · doi:10.1007/JHEP05(2011)036 |
| [19] | A.C. Wall, A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices, Phys. Rev.D 85 (2012) 104049 [Erratum ibid.D 87 (2013) 069904] [arXiv:1105.3445] [INSPIRE]. |
| [20] | A.C. Wall, Testing the generalized second law in 1 + 1 dimensional conformal vacua: an argument for the causal horizon, Phys. Rev.D 85 (2012) 024015 [arXiv:1105.3520] [INSPIRE]. |
| [21] | A.C. Wall, A survey of black hole thermodynamics, arXiv:1804.10610 [INSPIRE]. |
| [22] | Z.U. Khandker, S. Kundu and D. Li, Bulk matter and the boundary quantum null energy condition, JHEP08 (2018) 162 [arXiv:1803.03997] [INSPIRE]. · Zbl 1396.83009 · doi:10.1007/JHEP08(2018)162 |
| [23] | A. Almheiri and J. Polchinski, Models of AdS2backreaction and holography, JHEP11 (2015) 014 [arXiv:1402.6334] [INSPIRE]. · Zbl 1388.83079 |
| [24] | T.D. Chung and H.L. Verlinde, Dynamical moving mirrors and black holes, Nucl. Phys.B 418 (1994) 305 [hep-th/9311007] [INSPIRE]. · Zbl 1009.81525 |
| [25] | R. Bott, On the characteristic classes of groups of diffeomorphisms, Enseign. Math.23 (1977) 209. · Zbl 0367.57004 |
| [26] | T.G. Mertens, G.J. Turiaci and H.L. Verlinde, Solving the Schwarzian via the Conformal Bootstrap, JHEP08 (2017) 136 [arXiv:1705.08408] [INSPIRE]. · Zbl 1381.83089 · doi:10.1007/JHEP08(2017)136 |
| [27] | G. Turiaci and H. Verlinde, On CFT and quantum chaos, JHEP12 (2016) 110 [arXiv:1603.03020] [INSPIRE]. · Zbl 1390.81191 · doi:10.1007/JHEP12(2016)110 |
| [28] | J. Haegeman, T.J. Osborne, H. Verschelde and F. Verstraete, Entanglement renormalization for quantum fields in real space, Phys. Rev. Lett.110 (2013) 100402 [arXiv:1102.5524] [INSPIRE]. · doi:10.1103/PhysRevLett.110.100402 |
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