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.

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

References in corpus (6)

• Conformal collider physics: Energy and charge correlations
• Boundary Conformal Field Theory and a Boundary Central Charge
• The CFT/AdS correspondence, massive gravitons and a connectivity index conjecture
• Displacement Operators and Constraints on Boundary Central Charges
• 3d Abelian Gauge Theories at the Boundary
• General Bootstrap Equations in 4D CFTs

Cited by in corpus (4)

• Bootstrapping boundary-localized interactions II: Minimal models at the boundary
• 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