Finite temperature at finite places

A bstract 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 Witten 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.