Analyticity Properties of Graham-Witten Anomalies

Understand

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.