Abstract
We propose a 2D QFT generalization of the Sachdev-Ye-Kitaev model, which we argue preserves most of its features. The UV limit of the model is described by N copies of a topological Ising CFT. The full interacting model exhibits conformal symmetry in the IR and an emergent pseudo-Goldstone mode that arises from broken reparametrization symmetry. We find that the effective action of the Goldstone mode matches with the 3D AdS gravity action, viewed as a functional of the boundary metric. We compute the spectral density and show that the leading deviation from conformal invariance looks like a \( T\overline{T} \) deformation. We comment on the relation between the IR effective action and Liouville CFT.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Kitaev, Hidden Correlations in the Hawking Radiation and Thermal Noise, talk given at the 2015 Breakthrough Prize Fundamental Physics Symposium, Stanford University, Stanford, U.S.A., 10 November 2014 https://www.youtube.com/watch?v=OQ9qN8j7EZI.
A. Kitaev, Hidden correlations in the Hawking radiation and thermal noise, talk given at the KITP Theory Seminar, University of California, Santa Barbara, California, U.S.A., 12 February 2015 http://online.kitp.ucsb.edu/online/joint98/kitaev/.
A. Kitaev, A simple model of quantum holography. Part 1, talk given at the KITP Program: Entanglement in Strongly-Correlated Quantum Matter, University of California, Santa Barbara, California, U.S.A., 7 April-2 July 2015 http://online.kitp.ucsb.edu/online/entangled15/kitaev/.
A. Kitaev, A simple model of quantum holography. Part 2, talk given at the KITP Program: Entanglement in Strongly-Correlated Quantum Matter, University of California, Santa Barbara, California, U.S.A., 6 April-2 July 2015 http://online.kitp.ucsb.edu/online/entangled15/kitaev2/.
S. Sachdev, Bekenstein-Hawking Entropy and Strange Metals, Phys. Rev. X 5 (2015) 041025 [arXiv:1506.05111] [INSPIRE].
J. Polchinski and V. Rosenhaus, The Spectrum in the Sachdev-Ye-Kitaev Model, JHEP 04 (2016) 001 [arXiv:1601.06768] [INSPIRE].
J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].
S. Sachdev and J.-w. Ye, Gapless spin fluid ground state in a random, quantum Heisenberg magnet, Phys. Rev. Lett. 70 (1993) 3339 [cond-mat/9212030] [INSPIRE].
O. Parcollet and A. Georges, Non-fermi-liquid regime of a doped Mott insulator, Phys. Rev. B 59 (1999) 5341.
S. Sachdev, Holographic metals and the fractionalized Fermi liquid, Phys. Rev. Lett. 105 (2010) 151602 [arXiv:1006.3794] [INSPIRE].
O. Parcollet and A. Georges, Transition from overscreening to underscreening in the multichannel Kondo model: exact solution at large N , Phys. Rev. Lett. 79 (1997) 4665 [cond-mat/9707337].
O. Parcollet, A. Georges, G. Kotliar and A. Sengupta, Overscreened multichannel SU(N ) Kondo model: Large-N solution and conformal field theory, Phys. Rev. B 58 (1998) 3794 [cond-mat/9711192] [INSPIRE].
A. Jevicki, K. Suzuki and J. Yoon, Bi-Local Holography in the SYK Model, JHEP 07 (2016) 007 [arXiv:1603.06246] [INSPIRE].
A. Jevicki and K. Suzuki, Bi-Local Holography in the SYK Model: Perturbations, JHEP 11 (2016) 046 [arXiv:1608.07567] [INSPIRE].
K. Jensen, Chaos in AdS 2 Holography, Phys. Rev. Lett. 117 (2016) 111601 [arXiv:1605.06098] [INSPIRE].
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].
J. Engelsöy, T.G. Mertens and H. Verlinde, An investigation of AdS 2 backreaction and holography, JHEP 07 (2016) 139 [arXiv:1606.03438] [INSPIRE].
M. Cvetič and I. Papadimitriou, AdS 2 holographic dictionary, JHEP 12 (2016) 008 [Erratum JHEP 01 (2017) 120] [arXiv:1608.07018] [INSPIRE].
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].
D.J. Gross and V. Rosenhaus, A Generalization of Sachdev-Ye-Kitaev, JHEP 02 (2017) 093 [arXiv:1610.01569] [INSPIRE].
M. Berkooz, P. Narayan, M. Rozali and J. Simón, Higher Dimensional Generalizations of the SYK Model, JHEP 01 (2017) 138 [arXiv:1610.02422] [INSPIRE].
E. Witten, An SYK-Like Model Without Disorder, arXiv:1610.09758 [INSPIRE].
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].
M.B. Green and J.H. Schwarz, Covariant Description of Superstrings, Phys. Lett. B 136 (1984) 367 [INSPIRE].
A. Quelle, T. Kvorning, T.H. Hansson, and C. Morais Smith, Edge Majoranas on locally flat surfaces: The cone and the Möbius band, Phys. Rev. B 94 (2016) 125137 [arXiv:1606.06093].
V.G. Knizhnik, A.M. Polyakov and A.B. Zamolodchikov, Fractal Structure of 2D Quantum Gravity, Mod. Phys. Lett. A 3 (1988) 819 [INSPIRE].
R. Dijkgraaf, A geometrical approach to two-dimensional conformal field theory, Ph.D. Thesis, Utrecht The Netherlands (1989).
H.L. Verlinde, Conformal field theory, two-dimensional quantum gravity and quantization of Teichmüller space, Nucl. Phys. B 337 (1990) 652 [INSPIRE].
H.L. Verlinde and E.P. Verlinde, Conformal Field Theory And Geometric Quantization, in proceedings of the Trieste School and Workshop on Superstrings, Trieste, Italy, 3-14 April 1989, pp. 422-449 [IASSNS-HEP-89-58] [PUPT-89-1149] [https://lib-extopc.kek.jp/preprints/PDF/2000/0031/0031891.pdf] [INSPIRE].
E. Witten, On Holomorphic factorization of WZW and coset models, Commun. Math. Phys. 144 (1992) 189 [INSPIRE].
M. Blau and G. Thompson, Derivation of the Verlinde formula from Chern-Simons theory and the G/G model, Nucl. Phys. B 408 (1993) 345 [hep-th/9305010] [INSPIRE].
M. Fannes, B. Nachtergaele and R.F. Werner, Finitely correlated states on quantum spin chains, Commun. Math. Phys. 144 (1992) 443 [INSPIRE].
D. Perez-Garcia, F. Verstraete, M. Wolf, and J. Cirac, Matrix Product State Representations, Quantum Inf. Comput. 7 (2007) 401 [quant-ph/0608197] [http://www.rintonpress.com/journals/qiconline.html#v7n56].
W. Fu, D. Gaiotto, J. Maldacena and S. Sachdev, Supersymmetric Sachdev-Ye-Kitaev models, Phys. Rev. D 95 (2017) 026009 [Erratum ibid. D 95 (2017) 069904] [arXiv:1610.08917] [INSPIRE].
S. Dubovsky, R. Flauger and V. Gorbenko, Solving the Simplest Theory of Quantum Gravity, JHEP 09 (2012) 133 [arXiv:1205.6805] [INSPIRE].
F.A. Smirnov and A.B. Zamolodchikov, On space of integrable quantum field theories, Nucl. Phys. B 915 (2017) 363 [arXiv:1608.05499] [INSPIRE].
A. Cavaglià, S. Negro, I.M. Szécsényi and R. Tateo, \( T\overline{T} \) -deformed 2D Quantum Field Theories, JHEP 10 (2016) 112 [arXiv:1608.05534] [INSPIRE].
L. McGough, M. Mezei and H. Verlinde, Moving the CFT into the bulk with \( T\overline{T} \), arXiv:1611.03470 [INSPIRE].
A. Almheiri and J. Polchinski, Models of AdS 2 backreaction and holography, JHEP 11 (2015) 014 [arXiv:1402.6334] [INSPIRE].
L. Freidel, Reconstructing AdS/CFT, arXiv:0804.0632 [INSPIRE].
G. Turiaci and H. Verlinde, On CFT and Quantum Chaos, JHEP 12 (2016) 110 [arXiv:1603.03020] [INSPIRE].
S. Jackson, L. McGough and H. Verlinde, Conformal Bootstrap, Universality and Gravitational Scattering, Nucl. Phys. B 901 (2015) 382 [arXiv:1412.5205] [INSPIRE].
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
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1701.00528
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.
About this article
Cite this article
Turiaci, G.J., Verlinde, H. Towards a 2d QFT analog of the SYK model. J. High Energ. Phys. 2017, 167 (2017). https://doi.org/10.1007/JHEP10(2017)167
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2017)167