On the supersymmetric vacua of the Veneziano-Wosiek model

TL;DR

This paper analyzes the supersymmetric vacua of the Veneziano-Wosiek model at finite 't Hooft coupling, identifying phase transitions and providing explicit solutions for certain fermion sectors.

Contribution

It provides analytical solutions for F=2 vacua and supports the existence of a critical coupling at lambda=1 for F=4 vacua.

Findings

Two zero energy vacua for F=2 when lambda > 1

Identification of a critical point at lambda=1 separating different phases

Support for a phase transition at lambda=1 in the F=4 sector

Abstract

We study the supersymmetric vacua of the Veneziano-Wosiek model in sectors with fermion number F=2, 4 at finite 't Hooft coupling lambda. We prove that for F=2 there are two zero energy vacua for lambda > lambda_c = 1 and none otherwise. We give the analytical expressions of both vacua. One of them was previously known, the second one is obtained by solving the cohomology of the supersymmetric charges. At F=4 we compute the would-be supersymmetric vacua at high order in the the strong coupling expansion and provide strong support to the conclusion that lambda = 1 is a critical point in this sector too. It separates a strong coupling phase with two symmetric vacua from a weak coupling phase with positive spectrum.