# How a-type anomalies can depend on marginal couplings

## TL;DR

This paper explores how a-type anomalies in conformal field theories with defects depend on marginal couplings, revealing their anomalous one-point functions and the relation to the derivative of the a-anomaly.

## Contribution

It demonstrates the dependence of a-type anomalies on marginal couplings and relates one-point functions to the derivative of the a-anomaly via Wess-Zumino consistency.

## Key findings

- One-point functions of marginal operators are anomalous in the presence of defects.
- The Wess-Zumino consistency condition links these anomalies to the a-anomaly derivative.
- The constant term F for odd-dimensional surfaces can vary with marginal parameters.

## Abstract

Even dimensional defects and boundaries in conformal field theory support type $a$ anomalies on their world-volume. We show that the one-point functions of marginal operators, in the presence of defects and boundaries, are anomalous, and that the Wess-Zumino consistency condition relates them to the derivative of the $a$-anomaly with respect to the marginal coupling. We also argue that the constant term $F$ for odd dimensional surfaces can depend on marginal parameters.