Abstract
We consider \( \mathcal{N} \) = 2, 4 supersymmetric SYK models that have a peculiar low energy behavior, with the entropy going like S = S0 + (constant)Ta, where a ≠ 1. The large N equations for these models are a generalization of equations that have been previously studied as an unjustified truncation of the planar diagrams describing the BFSS matrix quantum mechanics or other related matrix models. Here we reanalyze these equations in order to better understand the low energy physics of these models. We find that the scalar fields develop large expectation values which explore the low energy valleys in the potential. The low energy physics is dominated by quadratic fluctuations around these values. These models were previously conjectured to have a spin glass phase. We did not find any evidence for this phase by using the usual diagnostics, such as searching for replica symmetry breaking solutions.
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Acknowledgments
We would like to thank T. Anous, L. Cugliandolo, D. Ghim, F. Haehl, D. Huse, Z. Komargodski, J. Kurchan, B. Swingle, M. Winer, and the participants of the Summer Simons workshop at Stony Brook for useful comments and suggestions.
J.M. is supported in part by U.S. Department of Energy grant DE-SC0009988. VN is supported in part by the US National Science Foundation under Grant No. PHY-2209997.
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ArXiv ePrint: 2309.08818v1
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Biggs, A., Maldacena, J. & Narovlansky, V. A supersymmetric SYK model with a curious low energy behavior. J. High Energ. Phys. 2024, 124 (2024). https://doi.org/10.1007/JHEP08(2024)124
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DOI: https://doi.org/10.1007/JHEP08(2024)124