Abstract
In this paper, we compute holographic Euclidean thermal correlators of the stress tensor and U(1) current from the AdS planar black hole. To this end, we set up perturbative boundary value problems for Einstein’s gravity and Maxwell theory in the spirit of Gubser-Klebanov-Polyakov-Witten, with appropriate gauge fixing and regularity boundary conditions at the horizon of the black hole. The linearized Einstein equation and Maxwell equation in the black hole background are related to the Heun equation of degenerate local monodromy. Leveraging the connection relation of local solutions of the Heun equation, we partly solve the boundary value problem and obtain exact two-point thermal correlators for U(1) current and stress tensor in the scalar and shear channels.
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Acknowledgments
We would like to thank Alba Grassi, Cristoforo Iossa, Yun-Ze Li, Hongfei Shu, Ashish Shukla and Yunda Zhang for their helpful discussion. S.H. would appreciate the financial support from the Fundamental Research Funds for the Central Universities and Max Planck Partner Group and the Natural Science Foundation of China (NSFC) Grants No. 12075101 and No. 12235016.
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He, S., Li, Y. Holographic Euclidean thermal correlator. J. High Energ. Phys. 2024, 24 (2024). https://doi.org/10.1007/JHEP03(2024)024
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DOI: https://doi.org/10.1007/JHEP03(2024)024