Derivation of an Abelian effective model for instanton chains in 3D Yang-Mills theory

TL;DR

This paper derives an Abelian effective model for instanton chains in 3D SU(2) Yang-Mills theory, focusing on monopoles, vortices, and dual fields, using polymer techniques to accurately model vortex interactions.

Contribution

It introduces a novel derivation of an Abelian model capturing monopole and vortex interactions in 3D Yang-Mills theory, employing polymer methods for ensemble representation.

Findings

Successful derivation of the Abelian model

Accurate representation of vortex end-to-end probabilities

Enhanced understanding of monopole-vortex interactions in 3D gauge theories

Abstract

In this work, we derive a recently proposed Abelian model to describe the interaction of correlated monopoles, center vortices, and dual fields in three dimensional SU(2) Yang-Mills theory. Following recent polymer techniques, special care is taken to obtain the end-to-end probability for a single interacting center vortex, which constitutes a key ingredient to represent the ensemble integration.