On the instantons and the hypermultiplet mass of N=2* super Yang-Mills on S^4

TL;DR

This paper clarifies the relationship between hypermultiplet mass and equivariant parameters in N=2* super Yang-Mills on S^4, showing no instanton contributions in N=4 theory and correcting previous claims about its correspondence to Liouville theory.

Contribution

It establishes the correct relation between hypermultiplet mass and equivariant parameters, and demonstrates the absence of instanton contributions in N=4 super Yang-Mills on S^4.

Findings

No instanton contributions in N=4 super Yang-Mills on S^4

Correct relation between hypermultiplet mass and equivariant parameters

N=4 SU(2) theory corresponds to Liouville theory with a non-trivial operator

Abstract

We show that the physical N=4 super Yang-Mills theory on a four-sphere with an arbitrary gauge group receives no instanton contributions, by clarifying the relation between the hypermultiplet mass and the equivariant parameters of the mass-deformed theory preserving N=2 supersymmetry. The correct relation also implies that N=4 superconformal Yang-Mills theory with gauge group SU(2) corresponds to Liouville theory on a torus with the insertion of a non-trivial operator, rather than the identity as have been claimed in the literature.