# $SU(2)$ gauge theory in the maximally abelian gauge without monopoles

## TL;DR

This paper introduces an algorithm for simulating $SU(2)$ lattice gauge theory in the maximally abelian gauge without monopoles, providing numerical evidence for nonperturbative monopole interactions and the non-connectedness of the Gribov region.

## Contribution

It presents a novel simulation algorithm for $SU(2)$ gauge theory in the MA gauge without monopoles and offers first numerical results supporting specific nonperturbative interactions.

## Key findings

- Nonperturbative interactions occur between monopoles and residual abelian fields.
- The Gribov region in the MA gauge is non-connected.
- Numerical results support the monopole interaction hypothesis.

## Abstract

We present an algorithm for simulation of $SU(2)$ lattice gauge theory under the MA gauge and first numerical results for the theory without abelian monopoles. The results support the idea that nonperturbative interaction arises between monopoles and residual abelian field and the other interactions are perturbative. It is shown that the Gribov region for the theory with the MA gauge fixed is non-connected.