Finiteness and anomalies in (4,0) supersymmetric sigma models

TL;DR

This paper confirms that (4,0) supersymmetric sigma models in two dimensions are finite up to three loops, using explicit calculations, and discusses the role of counterterms in maintaining supersymmetry and finiteness.

Contribution

It provides the first explicit three-loop verification of finiteness in (4,0) supersymmetric sigma models, supporting previous power-counting arguments.

Findings

Models are finite up to three loops.

Counterterms necessary for supersymmetry also ensure finiteness.

Power-counting arguments are validated by explicit calculations.

Abstract

Power-counting arguments based on extended superfields have been used to argue that two-dimensional supersymmetric sigma models with (4,0) supersymmetry are finite. This result is confirmed up to three loop order in pertubation theory by an explicit calculation using (1,0) superfields. In particular, it is shown that the finite counterterms which must be introduced into the theory in order to maintain (4,0) supersymmetry are precisely the terms that are required to establish ultra-violet finiteness.