Anomalies from correlation functions in defect conformal field theory

TL;DR

This paper investigates anomalies in correlation functions within defect conformal field theories, establishing links between boundary anomalies and bulk two-point functions across various dimensions, and generalizing previous results.

Contribution

It provides a detailed analysis of two-point functions involving marginal operators, the stress tensor, and displacement operators, and introduces a generalized anomaly effective action for higher-dimensional defects.

Findings

Boundary anomalies can be derived from bulk two-point functions.

Agreement between anomaly effective action and correlation functions is confirmed.

Generalization of anomaly relations to higher-dimensional defects is achieved.

Abstract

In previous work, we showed that an anomaly in the one point function of marginal operators is related by the Wess-Zumino condition to the Euler density anomaly on a two dimensional defect or boundary. Here we analyze in detail the two point functions of marginal operators with the stress tensor and with the displacement operator in three dimensions. We show how to get the boundary anomaly from these bulk two point functions and find perfect agreement with our anomaly effective action. For a higher dimensional conformal field theory with a four dimensional defect, we describe for the first time the anomaly effective action that relates the Euler density term to the one point function anomaly, generalizing our result for two dimensional defects.