Simplified Method for Trace Anomaly Calculations in d=6 and d<6

TL;DR

This paper introduces a simplified approach to calculating trace anomalies in six and lower dimensions, reducing computational complexity by combining lower-loop calculations on arbitrary geometries with higher-loop calculations on symmetric spaces.

Contribution

It presents a novel method that simplifies trace anomaly computations by combining lower-loop arbitrary geometry calculations with higher-loop symmetric space calculations.

Findings

The method reduces computational effort for trace anomalies in d=6.

It reproduces known anomaly results with fewer loops.

The approach is applicable to arbitrary geometries and symmetric spaces.

Abstract

We discuss a simplified method for computing trace anomalies in d=6 and d<6 dimensions. It is known that in the quantum mechanical approach trace anomalies in d dimensions are given by a (1+d/2)-loop computation in an auxiliary 1d sigma model with arbitrary geometry. We show how one can obtain the same information using a simpler d/2-loop calculation on an arbitrary geometry supplemented by a (1+d/2)-loop calculation on the simplified geometry of a maximally symmetric space.