A new approach to the two-dimensional $\sigma$-model with a topological charge

TL;DR

This paper introduces a dual transformation for the 2D sigma model with a topological charge, aiming to mitigate the sign problem and presenting preliminary numerical results and discussions.

Contribution

It presents a novel dual transformation based on character decomposition for the 2D sigma model with topological charge, potentially easing the sign problem.

Findings

Preliminary numerical results suggest potential benefits.

Discussion of remaining challenges in the approach.

Dual formulation offers new analytical insights.

Abstract

Based on character decomposition, a dual transformation is introduced leading to two formulations of the theory which should allow for a removal/softening of the sign problem in the original version. Very preliminar numerical results are commented and remaining problems discussed.