New modular invariance in the N=1* theory, operator mixings and supergravity singularities

We discuss the mass-deformed N = 4SU(N) supersymmetric Yang-Mills theory (a lso known as the N = 1* theory). We analyze how the correlation functions o f this theory transform under S-duality, and which correlation functions de pend holomorphically on the complexified gauge coupling tau. We provide exa ct modular-covariant expressions for the vacuum expectation values of chira l operators in the massive vacua of the N = 1* theory. We exhibit a novel m odular symmetry of the chiral sector of the theory in each vacuum, which ac ts on the coupling <(<tau>)over tilde> = (p tau + k)/q, where p, k and q ar e integers which label the different vacua. In the strong coupling limit, w e compare our results to the results of Polchinski and Strassler in the str ing theory dual of this theory, and find non-trivial agreement after operat or mixings are taken into account. In particular we find that their results are consistent with the predicted modular symmetry in <(<tau>)over tilde>. Our results imply that certain singularities found in solutions to five-di mensional gauged supergravity should not be resolvable in string theory, si nce there are no field theory vacua with corresponding vacuum expectation v alues in the large-N limit.