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arXiv:2409.10113 · Journal of High Energy Physics

Off-diagonal coupling of supersymmetric SYK model

Chenhao Zhang, Wenhe Cai

Published Feb 20, 2025• 0 citations
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Abstract

A bstract In this work, we consider the off-diagonal coupling between two supersymmetric SYK models, which preserves both supersymmetry and solvability. We found that the interaction terms of the N=2 supersymmetric SYK are holographically interpreted as a possible supersymmetric traversable wormhole. First, we introduce the coupling in the Homologic N=1 SYK model as a simplified example. Similar couplings can also be applied to the N=2 chiral SYK model with BPS states. We propose a special form of N=4 SYK by introducing supermultiplets, which also naturally include the coupling terms with additional symmetries. The N=4 holographic properties are investigated through the analysis of N=2 SYK theory. Furthermore, the effective actions are studied in both the thermal limit and the low-energy limit. We also investigate the SYK-like thermal field double states of the supersymmetric SYK model and the transmission amplitude between single-sided N=2 models in Lorentz time. Additionally, we study the multi-sided N=2,4 OTOCs.

DOI
10.1007/jhep02(2025)133

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A bstract In this work, we consider the off-diagonal coupling between two supersymmetric SYK models, which preserves both supersymmetry and solvability. We found that the interaction terms of the N=2 supersymmetric SYK are holographically interpreted as a possible supersymmetric traversable wormhole. First, we introduce the coupling in the Homologic N=1 SYK model as a simplified example. Similar couplings can also be applied to the N=2 chiral SYK model with BPS states. We propose a special form of N=4 SYK by introducing supermultiplets, which also naturally include the coupling terms with additional symmetries. The N=4 holographic properties are investigated through the analysis of N=2 SYK theory. Furthermore, the effective actions are studied in both the thermal limit and the low-energy limit. We also investigate the SYK-like thermal field double states of the supersymmetric SYK model and the transmission amplitude between single-sided N=2 models in Lorentz time. Additionally, we study the multi-sided N=2,4 OTOCs.
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In this thesis, we discuss the Sachdev-Ye-Kitaev (SYK) model and tensor models with similar properties. The SYK model is a quantum field theoretical model describing N interacting fermions, whose coupling constants are drawn from a Gaussian ensemble. Noteworthy properties of the SYK model include that it is analytically solvable in the large N limit, that it exhibits conformal symmetry at low energies and that it is maximally chaotic. These properties are remarkably similar to those of a 1 + 1 dimensional Schwarzschild black hole. It has been conjectured the SYK model is a holographic dual to the black hole. We introduce a set of Feynman rules for the SYK model. Using these rules, we show that in the large N limit the diagrams that contribute to the two-point function are all so-called iterated melonic diagrams. This allows us to derive a Schwinger-Dyson equation for the two-point function, which, in turn, can be solved exactly in the infrared limit. We also consider the four-point function. In the large N limit, the leading-order correction to the four-point function is given by so-called ladder diagrams. This allows us to derive an explicit expression for the four-point function. The SYK model can be generalized in a few different ways. In this thesis, we consider the generalization where the fermions act through q-fold interactions instead of quartic interactions present in the original SYK model. In particular, considerable simplifications can be achieved in the q → ∞ limit or q = 2 case, which we study. While the SYK model has many interesting properties, its random couplings limit its usability especially as a dual to a Schwarzschild black hole. We therefore also consider tensor models which do not have this drawback but manage to preserve the interesting properties of the SYK model. In the last chapter, we briefly inspect the chaotic behaviour of the SYK and tensor models and derive Lyapunov exponent for them. It can be shown that the expression saturates an upper bound for Lyapunov exponents of a large class of quantum systems, including large N systems.
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