Conformal Ward-Takahashi Identity at Finite Temperature

TL;DR

This paper derives finite-temperature conformal Ward-Takahashi identities, translating them into algebraic relations that determine two-point functions in momentum space consistent with thermal equilibrium conditions.

Contribution

It establishes a novel connection between conformal Ward-Takahashi identities and intertwining relations at finite temperature, leading to explicit solutions for two-point functions.

Findings

Derived recurrence relations for two-point functions

Solved relations to obtain thermal two-point functions

Ensured solutions satisfy KMS thermal equilibrium condition

Abstract

We study conformal Ward-Takahashi identities for two-point functions in $d(\geq3)$-dimensional finite-temperature conformal field theory. We first show that the conformal Ward-Takahashi identities can be translated into the intertwining relations of conformal algebra $\mathfrak{so}(2,d)$. We then show that, at finite temperature, the intertwining relations can be translated into the recurrence relations for two-point functions in complex momentum space. By solving these recurrence relations, we find the momentum-space two-point functions that satisfy the Kubo-Martin-Schwinger thermal equilibrium condition.