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arXiv · 2408.04199

Finite Temperature at Finite Places

An Huang·Christian Baadsgaard Jepsen
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Abstract

This paper studies AdS/CFT in its $p$-adic version (at the ``finite place") in the setting where the bulk geometry is made up of the Tate curve, a discrete quotient of the Bruhat-Tits tree. Generalizing a classic result due to Zabrodin, the boundary dual of the free massive bulk theory is explicitly derived. Introducing perturbative interactions, the Wittens diagrams for the two-point and three-point correlators are computed for generic scaling dimensions at one-loop and tree level respectively. The answers obtained demonstrate how $p$-adic AdS/CFT on the Tate curve provides a useful toy model for real CFTs at finite temperature.

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An Huang, Christian Baadsgaard Jepsen. 2024-08-08. Finite Temperature at Finite Places. https://doi.org/10.1007/jhep03(2025)097

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