# SO(3) vortices as a mechanism for generating a mass gap in the 2d SU(2) principal chiral model

## TL;DR

This paper introduces a mechanism involving SO(3) vortices that can generate a mass gap in the 2D SU(2) principal chiral model, supported by theoretical conditions and Monte Carlo evidence.

## Contribution

It establishes a novel link between SO(3) vortices and mass gap generation via an effective dual Ising model with an external magnetic field.

## Key findings

- Nonzero magnetic field in the effective Ising model implies a mass gap in the SU(2) system.
- Vortex correlation inequalities, if satisfied, lead to a nonzero effective magnetic field.
- Monte Carlo simulations support the plausibility of the correlation inequalities.

## Abstract

We propose a mechanism that can create a mass gap in the SU(2) chiral spin model at arbitrarily small temperatures. We give a sufficient condition for the mass gap to be non-zero in terms of the behaviour of an external Z(2) flux introduced by twisted boundary conditions. This condition in turn is transformed into an effective dual Ising model with an external magnetic field generated by SO(3) vortices. We show that having a nonzero magnetic field in the effective Ising model is sufficient for the SU(2) system to have a mass gap. We also show that certain vortex correlation inequalities, if satisfied, would imply a nonzero effective magnetic field. Finally we give some plausibility arguments and Monte Carlo evidence for the required correlation inequalities.