Title: On the instantons and the hypermultiplet mass of $ \mathcal{N} = {{2}^{ * }} $ super Yang-Mills on S 4
Abstract: We show that the physical $ \mathcal{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 $ \mathcal{N} = {2} $ supersymmetry. The correct relation also implies that $ \mathcal{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.