SO(3) vortices and disorder in the 2d SU(2) chiral model

TL;DR

This paper investigates how SO(3) vortices influence disorder in the 2d SU(2) chiral model, demonstrating their critical role in correlation decay at low temperatures and suggesting implications for 4d SU(2) gauge theories.

Contribution

It introduces a novel approach linking SO(3) vortices to correlation decay, providing both analytical proofs and Monte Carlo evidence for their role in disordering the model.

Findings

Vortices are crucial for correlation decay at low temperatures.

Certain vortex correlation inequalities imply exponential fall-off.

Monte Carlo simulations support the theoretical inequalities.

Abstract

We study the correlation function of the 2d SU(2) principal chiral model on the lattice. By rewriting the model in terms of Z(2) degrees of freedom coupled to SO(3) vortices we show that the vortices play a crucial role in disordering the correlations at low temperature. Using a series of exact transformations we prove that, if satisfied, certain inequalities between vortex correlations imply exponential fall-off of the correlation function at arbitrarily low temperatures. We also present some Monte Carlo evidence that these correlation inequalities are indeed satisfied. Our method can be easily translated to the language of 4d SU(2) gauge theory to establish the role of corresponding SO(3) monopoles in maintaining confinement at small couplings.