Stress Tensors from Trace Anomalies in Conformal Field Theories

TL;DR

This paper derives vacuum stress tensors in even-dimensional conformal field theories using trace anomalies, revealing a relation between Casimir energy and the type A anomaly coefficient, consistent with holographic predictions.

Contribution

It establishes a universal relation between Casimir energy and the type A anomaly coefficient in arbitrary even dimensions, extending previous two- and four-dimensional results.

Findings

Derived vacuum stress tensors from trace anomalies in even dimensions.

Established a relation between Casimir energy and the type A anomaly coefficient.

Confirmed consistency with holographic predictions across multiple dimensions.

Abstract

Using trace anomalies, we determine the vacuum stress tensors of arbitrary even dimensional conformal field theories in Weyl flat backgrounds. We demonstrate a simple relation between the Casimir energy on the real line times a sphere and the type A anomaly coefficient. This relation generalizes earlier results in two and four dimensions. These field theory results for the Casimir are shown to be consistent with holographic predictions in two, four, and six dimensions.