Abstract
We investigate a model closely related to both the original Sachdev-Ye-Kitaev (SYK) model and the \( \mathcal{N} \) = 1 supersymmetric SYK model. It consists of N real Majorana fermions and M auxiliary bosons with Yukawa interactions. We consider the large N and M limit and keep the ratio M/N fixed. The model has two branches characterized by the conformal dimensions of fields, which we compute as a function of the ratio M/N. One of the branches contains the supersymmetric saddle for M = N. As we take the limit M/N → ∞ both branches coincide and we obtain the same conformal dimensions as SYK. Furthermore, we determine the Lyapunov exponent of the model and find maximal chaos independent of M/N.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Kitaev, A simple model of quantum holography, talks at KITP, April 7, 2015 and May 27, 2015 [http://online.kitp.ucsb.edu/online/entangled15/kitaev/] [http://online.kitp.ucsb.edu/online/entangled15/kitaev2/].
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].
O. Parcollet and A. Georges, Non-Fermi liquid regime of a doped Mott insulator, Phys. Rev. B 59 (1999) 5341 [cond-mat/9806119].
A. Georges, O. Parcollet and S. Sachdev, Mean Field Theory of a Quantum Heisenberg Spin Glass, Phys. Rev. Lett. 85 (2000) 840 [cond-mat/9909239].
S.H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 03 (2014) 067 [arXiv:1306.0622] [INSPIRE].
S.H. Shenker and D. Stanford, Stringy effects in scrambling, JHEP 05 (2015) 132 [arXiv:1412.6087] [INSPIRE].
S. Sachdev, Holographic metals and the fractionalized Fermi liquid, Phys. Rev. Lett. 105 (2010) 151602 [arXiv:1006.3794] [INSPIRE].
J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, JHEP 08 (2016) 106 [arXiv:1503.01409] [INSPIRE].
S. Sachdev, Bekenstein-Hawking Entropy and Strange Metals, Phys. Rev. X 5 (2015) 041025 [arXiv:1506.05111] [INSPIRE].
A. Almheiri and J. Polchinski, Models of AdS 2 backreaction and holography, JHEP 11 (2015) 014 [arXiv:1402.6334] [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].
J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space, PTEP 2016 (2016) 12C104 [arXiv:1606.01857] [INSPIRE].
K. Jensen, Chaos in AdS 2 Holography, Phys. Rev. Lett. 117 (2016) 111601 [arXiv:1605.06098] [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].
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].
S.-K. Jian and H. Yao, Solvable Sachdev-Ye-Kitaev models in higher dimensions: from diffusion to many-body localization, Phys. Rev. Lett. 119 (2017) 206602 [arXiv:1703.02051] [INSPIRE].
J. Murugan, D. Stanford and E. Witten, More on Supersymmetric and 2d Analogs of the SYK Model, JHEP 08 (2017) 146 [arXiv:1706.05362] [INSPIRE].
G. Turiaci and H. Verlinde, Towards a 2d QFT Analog of the SYK Model, JHEP 10 (2017) 167 [arXiv:1701.00528] [INSPIRE].
D.J. Gross and V. Rosenhaus, A Generalization of Sachdev-Ye-Kitaev, JHEP 02 (2017) 093 [arXiv:1610.01569] [INSPIRE].
J. Yoon, Supersymmetric SYK Model: Bi-local Collective Superfield/Supermatrix Formulation, JHEP 10 (2017) 172 [arXiv:1706.05914] [INSPIRE].
Y. Chen, H. Zhai and P. Zhang, Tunable Quantum Chaos in the Sachdev-Ye-Kitaev Model Coupled to a Thermal Bath, JHEP 07 (2017) 150 [arXiv:1705.09818] [INSPIRE].
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].
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].
J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].
A. Kitaev and S.J. Suh, The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual, JHEP 05 (2018) 183 [arXiv:1711.08467] [INSPIRE].
D. Anninos, T. Anous and F. Denef, Disordered Quivers and Cold Horizons, JHEP 12 (2016) 071 [arXiv:1603.00453] [INSPIRE].
A.I. Larkin and Y.N. Ovchinnikov, Quasiclassical Method in the Theory of Superconductivity, Sov. Phys. JETP 28 (1969) 1200.
A. Almheiri, D. Marolf, J. Polchinski, D. Stanford and J. Sully, An Apologia for Firewalls, JHEP 09 (2013) 018 [arXiv:1304.6483] [INSPIRE].
A. Kitaev, Hidden correlations in the hawking radiation and thermal noise, talks at KITP, February 12, 2015 [http://online.kitp.ucsb.edu/online/joint98/kitaev/].
D.A. Roberts and D. Stanford, Two-dimensional conformal field theory and the butterfly effect, Phys. Rev. Lett. 115 (2015) 131603 [arXiv:1412.5123] [INSPIRE].
C. Peng, Vector models and generalized SYK models, JHEP 05 (2017) 129 [arXiv:1704.04223] [INSPIRE].
C. Peng, M. Spradlin and A. Volovich, Correlators in the \( \mathcal{N} \) = 2 Supersymmetric SYK Model, JHEP 10 (2017) 202 [arXiv:1706.06078] [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: 1808.01190
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Marcus, E., Vandoren, S. A new class of SYK-like models with maximal chaos. J. High Energ. Phys. 2019, 166 (2019). https://doi.org/10.1007/JHEP01(2019)166
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2019)166