Pole-skipping points in 2D gravity and SYK model

Haiming Yuan; Xian-Hui Ge; Keun-Young Kim; Chang-Woo Ji; Yongjun Ahn

doi:10.1007/JHEP08(2023)157

paper

Pole-skipping points in 2D gravity and SYK model

arXiv:2303.04801 · doi:10.1007/JHEP08(2023)157

Abstract

We represent the first investigation of pole-skipping on both the gravity and field theory sides. In contrast to the higher dimensional models, there is no momentum degree of freedom in $(1 + 1) -$ dimensional bulk theory. Thus, we then consider a scalar field mass as our degree of freedom for the pole-skipping phenomenon instead of momentum. The pole-skipping frequencies of the scalar field in 2D gravity are the same as higher dimensional cases: $ω = - i 2 π T n$ for positive integers $n$ . At each of these frequencies, there is a corresponding pole-skipping mass, so the pole-skipping points exist in $(ω, m)$ space. We also compute the pole-skipping points of the SYK model in $(ω, h)$ space where $h$ is the dimension of the bilinear primary operator. We find that there is a one-to-one correspondence of the pole-skipping points between the JT gravity and the SYK model. To obtain the pole-skipping points, we need to consider the parameter $ε$ related to the chemical potential on the horizon of charged JT gravity and the particle-hole asymmetric parameter $E$ of the complex SYK model as shift parameters. This highlights the $ε - E$ correspondence in relation to pole-skipping phenomenon.

Pole-skipping points in 2D gravity and SYK model

Abstract

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