Conformal Ward–Takahashi identity at finite temperature

Abstract

We study conformal Ward–Takahashi identities for two-point functions in d(≥3) -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 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.