A Sum Rule for Boundary Contributions to the Trace Anomaly

Abstract

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.

arXiv comment38 pages, 2 figures. v2 : added references; typos corrected, minor simplifications; matches published version

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• Fermions in Boundary Conformal Field Theory : Crossing Symmetry and $\epsilon$-Expansion
• Tensors and Spinors in de Sitter Space
• Boundaries in Free Higher Derivative Conformal Field Theories