Softly-Broken {\cal N} = 4 Supersymmetry in the Large-N Limit

TL;DR

This paper computes exact holomorphic observables in a mass-deformed { m N}=4 supersymmetric SU(N) Yang-Mills theory, revealing unexpected modular properties at large N and discussing implications for the AdS/CFT correspondence.

Contribution

It provides the first exact calculations of chiral condensates and domain wall tensions in the deformed { m N}=4 theory, uncovering novel modular behavior in the large-N limit.

Findings

Exact values of chiral condensates in massive vacua

Identification of anomalous SL(2,Z) modular properties

Insights into the AdS/CFT correspondence implications

Abstract

We calculate the exact values of the holomorphic observables of {\cal N}=4 supersymmetric SU(N) Yang-Mills theory deformed by mass terms which preserve {\cal N}=1 SUSY. These include the chiral condensates in each massive vacuum of the theory as well as the central charge which determines the tension of BPS saturated domain walls interpolating between these vacua. Several unexpected features emerge in the large-N limit, including anomalous modular properties under an SL(2,Z) duality group which acts on a complexification of the 't Hooft coupling \lambda=g^{2}N/4\pi. We discuss our results in the context of the AdS/CFT correspondence.