Light-ray sum rules and the c-anomaly

TL;DR

This paper derives a sum rule for the change in the c-anomaly coefficient in 4D quantum field theories, relating it to stress tensor three-point functions, extending previous results for the a-anomaly.

Contribution

It introduces a new sum rule for the c-anomaly coefficient, linking it to stress tensor correlators, and generalizes the understanding of anomaly flow in quantum field theories.

Findings

Sum rule for Δc in terms of stress tensor three-point function

Δa sum rule involves positive null energy expectation value

Δc sum rule involves off-diagonal matrix elements, no fixed sign

Abstract

In a four-dimensional quantum field theory that flows between two fixed points under the renormalization group, the change in the conformal anomaly $\Delta a$ has been related to the average null energy. We extend this result to derive a sum rule for the other anomaly coefficient, $\Delta c$, in terms of the stress tensor three-point function. While the sum rule for $\Delta a$ is an expectation value of the averaged null energy operator, and therefore positive, the result for $\Delta c$ involves the off-diagonal matrix elements, so it does not have a fixed sign.