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 = −i2πTn 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 \( \mathcal{E} \) of the complex SYK model as shift parameters. This highlights the ϵ − \( \mathcal{E} \) correspondence in relation to pole-skipping phenomenon.
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Acknowledgments
We would like to thank Sizheng Cao, Yu-Qi Lei, and Qing-Bing Wang for helpful discussions. This work is partly supported by NSFC, China (No. 12275166 and No.11875184). This work was also supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF-2021R1A2C1006791), the GIST Research Institute (GRI) and the AI-based GIST Research Scientist Project grant funded by the GIST in 2023.
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Yuan, H., Ge, XH., Kim, KY. et al. Pole-skipping points in 2D gravity and SYK model. J. High Energ. Phys. 2023, 157 (2023). https://doi.org/10.1007/JHEP08(2023)157
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DOI: https://doi.org/10.1007/JHEP08(2023)157