Boundary Anomalies and Correlation Functions

TL;DR

This paper explores how boundary anomalies influence stress tensor correlation functions in conformal field theories, revealing modifications to Ward identities and the role of boundary central charges in various geometries.

Contribution

It provides new insights into the relationship between boundary anomalies and stress tensor correlations, including effects on Ward identities and boundary central charges.

Findings

Boundary anomalies affect stress tensor correlation functions.

Modified conformal Ward identities due to boundary central charges.

Examples in spherical and cylindrical geometries illustrate the concepts.

Abstract

It was shown recently that boundary terms of conformal anomalies recover the universal contribution to the entanglement entropy and also play an important role in the boundary monotonicity theorem of odd-dimensional quantum field theories. Motivated by these results, we investigate relationships between boundary anomalies and the stress tensor correlation functions in conformal field theories. In particular, we focus on how the conformal Ward identity and the renormalization group equation are modified by boundary central charges. Renormalized stress tensors induced by boundary Weyl invariants are also discussed, with examples in spherical and cylindrical geometries.