Conformal Ward-Takahashi Identity at Finite Temperature

Abstract

We study conformal Ward-Takahashi identities for two-point functions in $d(\ge 3)$-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 $\mathfrak{so}(2,d)$. 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.

11 pages, 1 eepic figure, talk given at the Xth International Symposium on Quantum Theory and Symmetries (QTS-10), Varna, Bulgaria, 19-25 June 2017; typos corrected, references added

References in corpus (3)

• Implications of conformal invariance in momentum space
• Solving the Conformal Constraints for Scalar Operators in Momentum Space and the Evaluation of Feynman's Master Integrals
• Intertwining Operator in Thermal CFT${}_d$