Revisiting the k-theorem with the ANEC

Abstract: In the context of renormalization group flow of two dimensional unitary quantum field theories, the $c$-theorem is a cornerstone result. The $c$-theorem states that under renormalization group flow, the central charge of the UV CFT must always be greater than the central charge of the IR CFT. A lesser known cousin of the $c$-theorem is the $k$-theorem. Assuming that the theory has a $U(1)$ symmetry, one can define a current central charge $k$ based on the two-point function of the conserved current. The $k$-theorem then states that $k$ is also a renormalization group monotone.

Recently, using the averaged null energy condition (ANEC), Hartman and Mathys has shown not only the $c$-theorem but also its four dimensional relative -- the $a$ theorem. In this talk, we will extend this story to the $k$-theorem. The talk is based on the work done in 2511.17072.

condensed mattergeneral relativity and quantum cosmologyHEP - theorymathematical physicsdifferential geometry

Audience: advanced learners

( paper )

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Europe and Pacific Theoretical Physics

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