Weyl Anomaly in Higher Dimensions and Feynman Rules in Coordinate Space

TL;DR

This paper introduces an algorithm based on the heat-kernel method to compute Weyl anomalies in higher dimensions, providing Feynman rules in coordinate space and demonstrating the approach with a 6D scalar-gravity example.

Contribution

It presents a novel algorithm for calculating Weyl anomalies in higher dimensions using heat-kernel techniques and formulates Feynman rules in coordinate space.

Findings

Explicit Weyl anomaly result for 6D scalar-gravity theory

Development of Feynman rules in coordinate space

Introduction of graphical calculation methods

Abstract

An algorithm to obtain the Weyl anomaly in higher dimensions is presented. It is based on the heat-kernel method. Feynman rules, such as the vertex rule and the propagator rule, are given in (regularized) coordinate space. Graphical calculation is introduced. The 6 dimensional scalar-gravity theory is taken as an example, and its explicit result is obtained.