Light-ray sum rules and the c-anomaly

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