Pole-skipping points in 2D gravity and SYK model
Haiming Yuan, Xian-Hui Ge, Keunyoung Kim, Chang-Woo Ji, Yong jun Ahn
Abstract
A bstract 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 πTn 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 $$ \mathcal{E} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>E</mml:mi> </mml:math> of the complex SYK model as shift parameters. This highlights the ϵ − $$ \mathcal{E} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>E</mml:mi> </mml:math> correspondence in relation to pole-skipping phenomenon.