Abstract
We analyze real-time thermal correlation functions of conserved currents in holographic field theories using the grSK geometry, which provides a contour prescription for their evaluation. We demonstrate its efficacy, arguing that there are situations involving components of conserved currents, or derivative interactions, where such a prescription is, in fact, essential. To this end, we first undertake a careful analysis of the linearized wave equations in AdS black hole backgrounds and identify the branch points of the solutions as a function of (complexified) frequency and momentum. All the equations we study are Fuchsian with only regular singular points that for the most part are associated with the geometric features of the background. Special features, e.g., the appearance of apparent singular points at the horizon, whence outgoing solutions end up being analytic, arise at higher codimension loci in parameter space. Using the grSK geometry, we demonstrate that these apparent singularities do not correspond to any interesting physical features in higher-point functions. We also argue that the Schwinger-Keldysh collapse and KMS conditions, implemented by the grSK geometry, continue to hold even in the presence of such singularities. For charged black holes above a critical charge, we furthermore demonstrate that the energy density operator does not possess an exponentially growing mode, associated with ‘pole-skipping’, from one such apparent singularity. Our analysis suggests that the connection between the scrambling physics of black holes and energy transport has, at best, a limited domain of validity.
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Acknowledgments
We would like to thank Lorenz Eberhardt, Felix Haehl, Tom Hartman, Veronika Hubeny, Godwin Martin, Mark Mezei, and Omkar Shetye for valuable discussions. We also would like to thank an anonymous referee for suggestions and improvements to the presentation. RL acknowledges support of the Department of Atomic Energy, Government of India, under project no. RTI4001, and would also like to acknowledge his debt to the people of India for their steady and generous support to research in the basic sciences. MR would also like to thank ICTS, Bengaluru, and TIFR, Mumbai for hospitality during the course of this project. MR was supported by U.S. Department of Energy grant DE-SC0009999 and funds from the University of California. JV was supported by U.S. Department of Energy grant DE-SC0020360 under the HEP-QIS QuantISED program.
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Loganayagam, R., Rangamani, M. & Virrueta, J. Holographic thermal correlators: a tale of Fuchsian ODEs and integration contours. J. High Energ. Phys. 2023, 8 (2023). https://doi.org/10.1007/JHEP07(2023)008
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DOI: https://doi.org/10.1007/JHEP07(2023)008