Abstract
We study the pole-skipping phenomenon within holographic axion theories, a common framework for studying strongly coupled systems with chemical potential (μ) and momentum relaxation (β). Considering the backreaction characterized by μ and β, we encounter coupled equations of motion for the metric, gauge, and axion field, which are classified into spin-0, spin-1, and spin-2 channels. Employing gauge-invariant variables, we systematically address these equations and explore pole-skipping points within each sector using the near-horizon method. Our analysis reveals two classes of pole-skipping points: regular and singular pole-skipping points in which the latter is identified when standard linear differential equations exhibit singularity. Notably, pole-skipping points in the lower-half plane are regular, while those elsewhere are singular. This suggests that the pole-skipping point in the spin-0 channel, associated with quantum chaos, corresponds to a singular pole-skipping point. Additionally, we observe that the pole-skipping momentum, if purely real or imaginary for μ = β = 0, retains this characteristic for μ ≠ 0 and β ≠ 0.
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Acknowledgments
This work was 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 Ministry of Education (NRF-2020R1I1A2054376), and the AI-based GIST Research Scientist Project grant funded by the GIST in 2024. This work was also supported by Creation of the Quantum Information Science R&D Ecosystem (Grant No. 2022M3H3A106307411) through the National Research Foundation of Korea (NRF) funded by the Korean government (Ministry of Science and ICT). Y.A acknowledges the support of the Shanghai Municipal Science and Technology Major Project (Grant No.2019SHZDZX01). H.-S Jeong acknowledges the support of the Spanish MINECO “Centro de Excelencia Severo Ochoa” Programme under grant SEV-2012-0249. This work is supported through the grants CEX2020-001007-S and PID2021-123017NB-I00, funded by MCIN/AEI/10.13039/501100011033 and by ERDF A way of making Europe. V. Jahnke and
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Ahn, Y., Jahnke, V., Jeong, HS. et al. On pole-skipping with gauge-invariant variables in holographic axion theories. J. High Energ. Phys. 2024, 20 (2024). https://doi.org/10.1007/JHEP06(2024)020
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DOI: https://doi.org/10.1007/JHEP06(2024)020