Analyticity Properties of Graham-Witten Anomalies

TL;DR

This paper investigates the analytic structure of Graham-Witten anomalies, classifying them into types based on their origin and providing explicit verification in a specific scalar field model.

Contribution

It introduces a classification of Graham-Witten anomalies into internal and external types, linking them to type A or B Weyl anomalies, with explicit example verification.

Findings

External anomalies are all of type B.

Among internal anomalies, one is of type A and the rest are of type B.

Explicit check performed for a free scalar in 6D with a 2D submanifold.

Abstract

Analytic properties of Graham-Witten anomalies are considered. Weyl anomalies according to their analytic properties are of type A (coming from $\delta$-singularities in correlators of several energy-momentum tensors) or of type B (originating in counterterms which depend logarithmically on a mass scale). It is argued that all Graham-Witten anomalies can be divided into 2 groups: internal and external, and that all external anomalies are of type B, whereas among internal anomalies there is one term of type A and all the rest are of type B. This argument is checked explicitly for the case of a free scalar field in a 6-dimensional space with a 2-dimensional submanifold.