Superpotentials, quantum parameter space and phase transitions in N=1 supersymmetric gauge theories

TL;DR

This paper investigates the structure of superpotentials and phase transitions in large N dualities of N=1 SUSY U(N) gauge theories using spectral curves, revealing new insights into the quantum parameter space and phase transitions.

Contribution

It introduces a spectral curve approach to analyze superpotentials and phase transitions without relying on holomorphic matrix models, applied to the cubic model.

Findings

Characterization of critical spectral curves for phase transitions.

Analytic conditions for one-cut and two-cut phase transitions.

Mapping of phase transition curves in spectral and quantum parameter spaces.

Abstract

We study the superpotentials, quantum parameter space and phase transitions that arise in the study of large N dualities between $\mathcal{N}=1$ SUSY U(N) gauge theories and string models on local Calabi-Yau manifolds. The main tool of our analysis is a notion of spectral curve characterized by a set of complex partial 't Hooft parameters and cuts given by projections on the spectral curve of minimal supersymmetric cycles of the underlying Calabi-Yau manifold. In particular we show how prepotentials and superpotentials can be associated to spectral curves without relying on any holomorphic matrix model. As an application, we use a combination of analytical and numerical methods to study the cubic model, determine the analytic condition satisfied by critical one-cut spectral curves, and characterize the transition curves between the one-cut and two-cut phases both in the space of spectral curves and in the quantum parameter space.