Keldysh Wormholes and Anomalous Relaxation in the Dissipative Sachdev-Ye-Kitaev Model

• URL: http://arxiv.org/abs/2210.01695v3
• Date: Thu, 4 May 2023 09:33:55 GMT
• Title: Keldysh Wormholes and Anomalous Relaxation in the Dissipative Sachdev-Ye-Kitaev Model
• Authors: Antonio M. Garc\'ia-Garc\'ia, Lucas S\'a, Jacobus J. M. Verbaarschot, and Jie Ping Zheng
• Abstract summary: We study the out-of-equilibrium dynamics of a Sachdev-Ye-Kitaev (SYK) model, $N$ fermions with a $q$-body interaction of infinite range, coupled to a Markovian environment. Close to the infinite-temperature steady state, the real-time Lindbladian dynamics of this system is identical to the near-zero-temperature dynamics in Euclidean time. We identify a potential gravity dual of the real-time dissipative SYK model: a double-trumpet configuration in a near-de Sitter space in two dimensions with matter
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the out-of-equilibrium dynamics of a Sachdev-Ye-Kitaev (SYK) model, $N$ fermions with a $q$-body interaction of infinite range, coupled to a Markovian environment. Close to the infinite-temperature steady state, the real-time Lindbladian dynamics of this system is identical to the near-zero-temperature dynamics in Euclidean time of a two-site non-Hermitian SYK with intersite coupling whose gravity dual has been recently related to wormhole configurations. We show that the saddle-point equations in the real-time formulation are identical to those in Euclidean time. Indeed, an explicit calculation of Green's functions at low temperature, numerical for $q = 4$ and analytical for $q = 2$ and large $q$, illustrates this equivalence. Only for very strong coupling does the decay rate approach the linear dependence on the coupling characteristic of a dissipation-driven approach to the steady state. For $q > 2$, we identify a potential gravity dual of the real-time dissipative SYK model: a double-trumpet configuration in a near-de Sitter space in two dimensions with matter. This configuration, which we term a Keldysh wormhole, is responsible for a finite decay rate even in the absence of coupling to the environment.

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