On three-dimensional trace anomaly from holographic local RG

TL;DR

This paper investigates three-dimensional quantum field theories with external fields using holographic local RG, revealing conditions under which trace anomalies vanish at fixed points and clarifying their origins.

Contribution

It provides an explicit holographic computation of the stress tensor trace in 3D QFTs and analyzes the behavior of anomalies and beta functions at fixed points.

Findings

Trace anomalies vanish at fixed points.

Vector beta functions satisfy Wess-Zumino conditions.

Anomalies are absent due to specific structural reasons.

Abstract

Odd-dimensional quantum field theories (QFTs) can have nonzero trace anomalies if external fields are introduced and some ingredients needed to make Lorentz scalars with appropriate mass dimensions (or weights) are supplied. We have studied a three-dimensional QFT and explicitly computed the trace of the stress tensor using the holographic local renormalization group (RG). We have checked some properties of vector beta functions and the Wess-Zumino consistency condition, however, found the anomalies vanish on fixed points. We clarify what is responsible for the vanishing trace anomalies.