A sum rule for boundary contributions to the trace anomaly

In the context of boundary conformal field theory, we derive a sum rule that relates two and three point functions of the displacement operator. For four dimensional conformal field theory with a three dimensional boundary, this sum rule in turn relates the two boundary contributions to the anomaly in the trace of the stress tensor. We check our sum rule for a variety of free theories and also for a weakly interacting theory, where a free scalar in the bulk couples marginally to a generalized free field on the boundary.

Automated summary

In the context of boundary conformal field theory, a sum rule is derived that relates the two and three point functions of the displacement operator. For four dimensional conformal field theory with a three-dimensional boundary, this sum rule further relates the two boundary contributions to the anomaly in the trace of the stress tensor.