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

TL;DR

This paper investigates the modular properties of the N=1* supersymmetric Yang-Mills theory, providing exact expressions for operator expectation values, revealing a novel modular symmetry, and comparing results with string theory duals to understand supergravity singularities.

Contribution

It introduces a new modular symmetry acting on the coupling in the N=1* theory and provides exact modular-covariant vacuum expectation values of chiral operators.

Findings

Discovered a novel modular symmetry in the chiral sector of the N=1* theory.

Derived exact modular-covariant expressions for vacuum expectation values.

Found agreement with string theory dual results after accounting for operator mixings.

Abstract

We discuss the mass-deformed N=4 SU(N) supersymmetric Yang-Mills theory (also known as the N=1* theory). We analyze how the correlation functions of this theory transform under S-duality, and which correlation functions depend holomorphically on the complexified gauge coupling \tau. We provide exact modular-covariant expressions for the vacuum expectation values of chiral operators in the massive vacua of the N=1* theory. We exhibit a novel modular symmetry of the chiral sector of the theory in each vacuum, which acts on the coupling ${\tilde \tau}= (p\tau+k)/q$, where p, k and q are integers which label the different vacua. In the strong coupling limit, we compare our results to the results of Polchinski and Strassler in the string theory dual of this theory, and find non-trivial agreement after operator mixings are taken into account. In particular we find that their results are consistent with the predicted modular symmetry in ${\tilde \tau}$. Our results imply that certain singularities found in solutions to five dimensional gauged supergravity should not be resolvable in string theory, since there are no field theory vacua with corresponding vacuum expectation values in the large N limit.