Loops Outside a Black Hole

R. Loganayagam; Godwin Martin; Shivam K. Sharma

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arXiv · 2509.03656

Loops Outside a Black Hole

R. Loganayagam·Godwin Martin·Shivam K. Sharma

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Abstract

We present a general conjecture for evaluating multiple discontinuity integrals arising from bulk loop diagrams in the gravitational Schwinger-Keldysh geometry. This generalises earlier tree-level results in arXiv:2403.10654 to arbitrary bulk loops with no tadpoles (for scalar non-derivative interactions). The conjectured result takes the form of loop integrals performed in a real-time finite-temperature field theory living on the exterior of the black hole. We check our conjecture against all one-loop and many two and three-loop contributions to two, three, and four-point functions. Our diagrammatic rules for the exterior field theory are consistent with microscopic unitarity and thermality at arbitrary loop level. We also remark on a novel approach to real-time finite-temperature holography based on bulk Schwinger-Dyson equations, with the vertices integrated over the black hole exterior.

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R. Loganayagam, Godwin Martin, Shivam K. Sharma. 2025-09-03. Loops Outside a Black Hole. https://arxiv.org/abs/2509.03656

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