Large N transition in the 2D SU(N)xSU(N) nonlinear sigma model

TL;DR

This paper investigates a phase transition in the characteristic polynomial of the two-point function in a 2D large N principal chiral model, revealing a universality class shared with 2D large N QCD.

Contribution

It demonstrates a large N transition in the characteristic polynomial of a 2D principal chiral model, connecting it to known universality classes in large N QCD.

Findings

Transition occurs at a critical distance proportional to the correlation length.

The transition belongs to the same universality class as 2D large N QCD.

Numerical evidence supports the existence of this phase transition.

Abstract

We consider the characteristic polynomial associated with the smoothed two point function in two dimensional large N principal chiral model. We numerically show that it undergoes a transition at a critical distance of the order of the correlation length. The transition is in the same universality class as two dimensional large N QCD.