Phase structure and critical processes of spectral curves in large N dualities

TL;DR

This paper analyzes the phase structure of spectral curves in large N dualities, providing a detailed description of the one-cut phase, critical conditions, and an algorithm for two-cut curves in the cubic model.

Contribution

It offers a comprehensive analytical and numerical study of spectral curves in large N dualities, including phase descriptions and computational algorithms.

Findings

Complete description of the one-cut phase in the cubic model

Analytic conditions for critical spectral curves

Algorithm for calculating two-cut spectral curves

Abstract

We examine the phase structure and the critical processes of the spectral curves that arise in the study of large N dualities between supersymmetric Yang-Mills theories and string models on local Calabi-Yau manifolds. These spectral curves are determined by a set of complex partial 't Hooft parameters and a system of cuts given by projections on the spectral curve of minimal supersymmetric cycles of the underlying Calabi-Yau manifold. Using a combination of analytical and numerical methods we give a complete description of the one-cut phase in the cubic model, determine the analytic condition satisfied by critical one-cut spectral curves, and give an algorithm to calculate the two-cut spectral curves of the cubic model for generic values of the partial 't Hooft parameters.