An N=1 duality cascade from a deformation of N=4 SUSY Yang-Mills

TL;DR

This paper explores a specific N=1 superconformal theory derived from N=4 SUSY Yang-Mills, revealing a duality cascade leading to a confining phase, with exact quantum deformations of the classical moduli space computed via a holomorphic matrix model.

Contribution

It provides an exact solution for the quantum superpotential and describes the deformation of the classical moduli space in a duality cascade scenario.

Findings

Exact quantum superpotential computed at the cascade endpoint

Classical conifold singularities are replaced by finite three-cycles

Global geometry differs from the local deformed conifold structure

Abstract

We study relevant deformations of an N=1 superconformal theory which is an exactly marginal deformation of U(N) N=4 SUSY Yang-Mills. The resulting theory has a classical Higgs branch that is a complex deformation of the orbifold C^3/Z_n x Z_n that is a non-compact Calabi-Yau space with isolated conifold singularities. At these singular points in moduli space the theory exhibits a duality cascade and flows to a confining theory with a mass gap. By exactly solving the corresponding holomorphic matrix model we compute the exact quantum superpotential generated at the end of the duality cascade and calculate precisely how quantum effects deform the classical moduli space by replacing the conifold singularities with three-cycles of finite size. Locally the structure is that of the deformed conifold, but the global geometry is different. This desingularized quantum deformed geometry is the moduli space of probe D3-branes at the end of a duality cascade realized on the worldvolume of (fractional) D3-branes placed at the isolated conifold singularities in the deformation of the orbifold C^3/Z_n x Z_n with discrete torsion.