[PDF] https://doi.org/10.3952/physics.v59i2.4013

Open access article / Atviros prieigos straipsnis
Lith. J. Phys. 59, 104–112 (2019)
 


ON A (PSEUDO)HOLOGRAPHIC NATURE OF THE SYK-LIKE MODELS
 
Dmitri V. Khveshchenko
  Department of Physics and Astronomy, University of North Carolina, Chapel Hill, NC 27599, U.S.A
Email: khvesh@physics.unc.edu

Received 13 May 2019; accepted 21 June 2019

Some generalizations of the Sachdev–Ye–Kitaev (SYK) model and different patterns of their reparametrization symmetry breaking are discussed. The analysis of such (pseudo)holographic systems relates their generalized one-dimensional Schwarzian dynamics to (quasi) two-dimensional Liouvillian quantum mechanics. As compared to the original SYK case, the latter might be dissipative or have discrete states in its spectrum, either of which properties alters thermodynamics and correlations while preserving the underlying SL(2, R) symmetry.
Keywords: Sachdev–Ye–Kitaev (SYK) model, holographic systems, Schwarzian dynamics

APIE (PSEUDO)HOLOGRAFINĘ SYK TIPO MODELIŲ PRIGIMTĮ
Dmitri V. Khveshchenko

Šiaurės Karolinos universiteto Fizikos ir astronomijos fakultetas, Čapel Hilas, Šiaurės Karolina, JAV
 

References / Nuorodos

[1] S. Sachdev and J. Ye, Gapless spin-fluid ground state in a random, quantum Heisenberg magnet, Phys. Rev. Lett. 70, 3339 (1993),
https://doi.org/10.1103/PhysRevLett.70.3339
[2] S. Sachdev, Holographic metals and the fractionalized Fermi liquid, Phys. Rev. Lett. 105, 151602 (2010),
https://doi.org/10.1103/PhysRevLett.105.151602
[3] S. Sachdev, Bekenstein-Hawking entropy and strange metals, Phys. Rev. X 5, 041025 (2015),
https://doi.org/10.1103/PhysRevX.5.041025
[4] A. Kitaev, KITP seminars (2015),
https://online.kitp.ucsb.edu/online/joint98/kitaev/
[5] A. Kitaev, Notes on SL˜(2,)\widetilde{\mathrm{SL}}(2,ℝ) representations,
https://arxiv.org/abs/1711.08169
[6] A. Kitaev and S.J. Suh, The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual, J. High Energy Phys. 2018(05), 183 (2018),
https://doi.org/10.1007/JHEP05(2018)183
[7] A. Kitaev, Statistical mechanics of a two-dimensional black hole,
https://arxiv.org/abs/1808.07032
[8] E. Witten, An SYK-like model without disorder,
https://arxiv.org/abs/1610.09758
[9] R. Gurau, The complete 1/N expansion of a SYK–like tensor model,
https://arxiv.org/abs/1611.04032
[10] R. Gurau, The ıε\imath ε prescription in the SYK model,
https://arxiv.org/abs/1705.08581
[11] I.R. Klebanov and G. Tarnopolsky, Uncolored random tensors, melon diagrams, and the Sachdev-Ye-Kitaev models, Phys. Rev. D 95, 046004 (2017),
https://doi.org/10.1103/PhysRevD.95.046004
[12] S. Giombi, I.R. Klebanov, and G. Tarnopolsky, Bosonic tensor models at large N and small ε, Phys. Rev. D 96, 106014 (2017),
https://doi.org/10.1103/PhysRevD.96.106014
[13] M. Ammon and J. Erdmenger, Gauge/Gravity Duality: Foundations and Applications (Cambridge University Press, 2015),
https://doi.org/10.1017/CBO9780511846373
[14] J. Zaanen, Y. Liu, Y.-W. Sun, and K. Schalm, Holographic Duality in Condensed Matter Physics (Cambridge University Press, 2015),
https://doi.org/10.1017/CBO9781139942492
[15] S. Hartnoll, A. Lucas, and S. Sachdev, Holographic Quantum Matter (MIT Press, 2018),
https://mitpress.mit.edu/books/holographic-quantum-matter
[16] J. Maldacena, S.H. Shenker, and D. Stanford, A bound on chaos, J. High Energy Phys. 2016(08), 106 (2016),
https://doi.org/10.1007/JHEP08(2016)106
[17] J. Maldacena and D. Stanford, Comments on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94(10), 106002 (2016),
https://doi.org/10.1103/PhysRevD.94.106002
[18] 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(12), 12C104 (2016),
https://doi.org/10.1093/ptep/ptw124
[19] D. Stanford and E. Witten, Fermionic localization of the Schwarzian theory, J. High Energy Phys. 2017(10), 008 (2017),
https://doi.org/10.1007/JHEP10(2017)008
[20] J. Polchinski and V. Rosenhaus, The spectrum in the Sachdev-Ye-Kitaev model, J. High Energy Phys. 2016(04), 001 (2016),
https://doi.org/10.1007/JHEP04(2016)001
[21] D.J. Gross and V. Rosenhaus, The bulk dual of SYK: cubic couplings, J. High Energy Phys. 2017(05), 092 (2017),
https://doi.org/10.1007/JHEP05(2017)092
[22] D.J. Gross and V. Rosenhaus, All point correlation functions in SYK, J. High Energy Phys. 2017(12), 148 (2017),
https://doi.org/10.1007/JHEP12(2017)148
[23] G. Sárosi, AdS2 holography and the SYK model,
https://arxiv.org/abs/1711.08482
[24] H.W. Lin, J. Maldacena, and Y. Zhao, Symmetries near the horizon,
https://arxiv.org/abs/1904.12820
[25] D.V. Khveshchenko, Taking a critical look at holographic critical matter, Lith. J. Phys. 55, 208 (2015),
https://doi.org/10.3952/physics.v55i3.3150
[26] D.V. Khveshchenko, Demystifying the holographic mystique, Lith. J. Phys. 56, 125 (2016),
https://doi.org/10.3952/physics.v56i3.3363
[27] S. Caracciolo, M.A. Cardella, and M. Pastore, Remarks on replica diagonal collective field condensations in SYK,
https://arxiv.org/abs/1807.10213
[28] I.Ya. Aref'eva, M.A. Khramtsov, M.D. Tikhanovskaya, and I.V. Volovich, On replica-nondiagonal large N saddles in the SYK model, EPJ Web Conf. 191, 06007 (2018),
https://doi.org/10.1051/epjconf/201819106007
[29] H. Wang, D. Bagrets, A.L. Chudnovskiy, and A. Kamenev, On the replica structure of Sachdev-Ye-Kitaev model,
https://arxiv.org/abs/1812.02666
[30] G. Gur-Ari, R. Mahajan, and A. Vaezi, Does the SYK model have a spin glass phase?,
https://arxiv.org/abs/1806.10145
[31] D.V. Khveshchenko, Thickening and sickening the SYK model, SciPost Phys. 5, 012 (2018),
https://doi.org/10.21468/SciPostPhys.5.1.012
[32] D.V. Khveshchenko, Seeking to develop global SYK-ness, Condens. Matter 3(4), 40 (2018),
https://doi.org/10.3390/condmat3040040
[33] Y. Gu, X-L. Qi, and D. Stanford, Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models, J. High Energy Phys. 2017(05), 125 (2017),
https://doi.org/10.1007/JHEP05(2017)125
[34] Y. Gu, A. Lucas, and X-L. Qi, Energy diffusion and the buttery effect in inhomogeneous Sachdev-Ye-Kitaev chains, SciPost Phys. 2, 018 (2017),
https://doi.org/10.21468/SciPostPhys.2.3.018
[35] Y. Gu, A. Lucas, and X.-L. Qi, Spread of entanglement in a Sachdev-Ye-Kitaev chain, J. High Energy Phys. 2017(09), 120 (2017),
https://doi.org/10.1007/JHEP09(2017)120
[36] Y. Gu and A. Kitaev, On the relation between the magnitude and exponent of OTOCs, J. High Energy Phys. 2019(02), 75 (2019),
https://doi.org/10.1007/JHEP02(2019)075
[37] V. Bonzom, L. Lionni, and A. Tanasa, Diagrammatics of a colored SYK model and of an SYK-like tensor model, leading and next-to-leading orders, J. Math. Phys. 58(5), 052301 (2017),
https://doi.org/10.1063/1.4983562
[38] D. Benedetti and R. Gurau, 2PI effective action for the SYK model and tensor field theories, J. High Energy Phys. 2018(05), 156 (2018),
https://doi.org/10.1007/JHEP05(2018)156
[39] D. Bagrets, A. Altland, and A. Kamenev, Sachdev-Ye-Kitaev model as Liouville quantum mechanics, Nucl. Phys. B 911, 191 (2016),
https://doi.org/10.1016/j.nuclphysb.2016.08.002
[40] D. Bagrets, A. Altland, and A. Kamenev, Power-law out of time order correlation functions in the SYK model, Nucl. Phys. B 921, 727 (2017),
https://doi.org/10.1016/j.nuclphysb.2017.06.012
[41] T.G. Mertens, G.J. Turiaci, and H.L. Verlinde, Solving the Schwarzian via the conformal bootstrap, J. High Energy Phys. 2017(08), 136 (2017),
https://doi.org/10.1007/JHEP08(2017)136
[42] T.G. Mertens, The Schwarzian theory — origins, J. High Energy Phys. 2018(05), 36 (2018),
https://doi.org/10.1007/JHEP05(2018)036
[43] Z. Yang, The quantum gravity dynamics of near extremal black holes,
https://arxiv.org/abs/1809.08647
[44] A. Blommaert, T.G. Mertens, and H. Verschelde, The Schwarzian theory — a Wilson line perspective, J. High Energy Phys. 2018(12), 22 (2018),
https://doi.org/10.1007/JHEP12(2018)022
[45] A. Blommaert, T.G. Mertens, and H. Verschelde, Fine structure of Jackiw-Teitelboim quantum gravity,
https://arxiv.org/abs/1812.00918
[46] A. Comtet and P.J. Houston, Effective action on the hyperbolic plane in a constant external field, J. Math. Phys. 26, 185 (1985),
https://doi.org/10.1063/1.526781
[47] A. Comtet, On the Landau levels on the hyperbolic plane, Ann. Phys. 173, 185 (1987),
https://doi.org/10.1016/0003-4916(87)90098-4
[48] A. Jevicki, K. Suzuki, and J. Yoon, Bi-local holography in the SYK model, J. High Energy Phys. 2016(07), 7 (2016),
https://doi.org/10.1007/JHEP07(2016)007
[49] A. Jevicki and K. Suzuki, Bi-local holography in the SYK model: perturbations, J. High Energy Phys. 2016(11), 46 (2016),
https://doi.org/10.1007/JHEP11(2016)046
[50] S.R. Das, A. Jevicki, and K. Suzuki, Three dimensional view of the SYK/AdS duality, J. High Energy Phys. 2017(09), 17 (2017),
https://doi.org/10.1007/JHEP09(2017)017
[51] S.R. Das, A. Ghosh, A. Jevicki, and K. Suzuki, Spacetime in the SYK model, J. High Energy Phys. 2018(07), 184 (2018),
https://doi.org/10.1007/JHEP07(2018)184
[52] S.R. Das, A. Ghosh, A. Jevicki, and K. Suzuki, Three dimensional view of arbitrary q SYK models, J. High Energy Phys. 2018(02), 162 (2018),
https://doi.org/10.1007/JHEP02(2018)162
[53] M. Laskin, T. Can, and P. Wiegmann, Collective field theory for quantum Hall states, Phys. Rev. B 92, 235141 (2015),
https://doi.org/10.1103/PhysRevB.92.235141
[54] M. Laskin, Y.H. Chiu, T. Can, and P. Wiegmann, Emergent conformal symmetry and geometric transport properties of quantum Hall states on singular surfaces, Phys. Rev. Lett. 117, 266803 (2016),
https://doi.org/10.1103/PhysRevLett.117.266803
[55] S. Klevtsov, X. Ma, G. Marinescu, and P. Wiegmann, Quantum Hall effect and Quillen metric, Commun. Math. Phys. 349, 819–855 (2017),
https://doi.org/10.1007/s00220-016-2789-2
[56] G. Mandal, P. Nayak, and S.R. Wadia, Coadjoint orbit action of Virasoro group and two-dimensional quantum gravity dual to SYK/tensor models, J. High Energy Phys. 2017(11), 46 (2017),
https://doi.org/10.1007/JHEP11(2017)046
[57] A. Gaikwad, L.K. Joshi, G. Mandal, and S.R. Wadia, Holographic dual to charged SYK from 3D gravity and Chern-Simons,
https://arxiv.org/abs/1802.07746
[58] T.G. Mertens and G.J. Turiaci, Defects in Jackiw-Teitelboim quantum gravity,
https://arxiv.org/abs/1904.05228