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.

Conformal boundary conditions for a 4d scalar field

“…6. As noted in [6], there is a universal prediction for C D as a function of a Φ 2 coming from the coupling to mean-field theory on the boundary [17,31,32], and our calculation at the leading order at large N f simply reproduces this universal curve as we vary κ.…”

The Tilting Space of Boundary Conformal Field Theories

“…We have introduced the normalization κ −1 = (d − 2) Vol(S d−1 ) and the mirror point x = (−x ⊥ , x ). This result can be reproduced by treating the moduli using conformal perturbation theory [10,11]. In the boundary limit, we can then read off…”

Tensors and Spinors in de Sitter Space

“…Pushing this analogy further would be an interesting pursuit. One could also, in the Euclidean picture, consider the construction of isometry generators through topological surface operators, as in BCFT [85], with the hope of new insights on Ward identities and asymptotic symmetries in dS [68][69][70][71]. Another possible extension is to make contact between our formalism and the one developed for massless fields [86], and the similar spinor helicities for CFT 3 [87].…”