# Holographic calculation of boundary terms in conformal anomaly

## TL;DR

This paper computes boundary contributions to the conformal anomaly in boundary conformal field theories using holographic methods, emphasizing the role of supersymmetry in the ${
m N}=4$ SYM context.

## Contribution

It provides a holographic derivation of boundary terms in the conformal anomaly for $d=3$ and $d=4$, including the impact of supersymmetry.

## Key findings

- Holographic calculation of boundary conformal anomaly terms in $d=3$ and $d=4$.
- Identification of the role of supersymmetry in boundary anomaly calculations.
- Comparison of two holographic prescriptions for boundary CFTs.

## Abstract

In the presence of boundaries the integrated conformal anomaly is modified by the boundary terms so that the anomaly is non-vanishing in any (even or odd) dimension. The boundary terms are due to extrinsic curvature whose exact structure in $d=3$ and $d=4$ has recently been identified. In this note we present a holographic calculation of those terms in two different prescriptions for the holographic description of the boundary CFT. We stress the role of supersymmetry when discussing the holographic description of ${\cal N}=4$ SYM on a $4$-manifold with boundaries.