Boundary conformal invariants and the conformal anomaly in five dimensions

TL;DR

This paper analyzes the boundary conformal invariants and the conformal anomaly in five-dimensional spaces, identifying new invariants and calculating the anomaly for scalar fields with specific boundary conditions.

Contribution

It provides a complete list of boundary conformal invariants in five dimensions, including a newly discovered invariant involving derivatives of extrinsic curvature.

Findings

Identified a new boundary conformal invariant with derivatives of extrinsic curvature.

Computed the conformal anomaly for scalar fields with Dirichlet and Robin boundary conditions.

Determined the boundary conformal charges associated with the anomaly.

Abstract

In odd dimensions the integrated conformal anomaly is entirely due to the boundary terms \cite{Solodukhin:2015eca}. In this paper we present a detailed analysis of the anomaly in five dimensions. We give the complete list of the boundary conformal invariants that exist in five dimensions. Additionally to 8 invariants known before we find a new conformal invariant that contains the derivatives of the extrinsic curvature along the boundary. Then, for a conformal scalar field satisfying either the Dirichlet or the conformal invariant Robin boundary conditions we use the available general results for the heat kernel coefficient $a_5$, compute the conformal anomaly and identify the corresponding values of all boundary conformal charges.