Probing the Yang-Mills vacuum with adjoint zero-modes

TL;DR

This paper explores using adjoint Dirac operator modes to filter and analyze the topological structures in Yang-Mills theories, effectively distinguishing long-range features from short-range fluctuations.

Contribution

It implements and tests a method that associates Weyl fermionic modes in the adjoint representation to gauge configurations for topological analysis.

Findings

Successful filtering of gauge field topologies

Effective separation of self-dual and anti self-dual components

Validation on initial gauge configurations

Abstract

For the non-perturbative analysis of the topological content of Yang-Mills theories, it is essential to disentangle long-range structures from short-range fluctuations. Some time ago, one of us proposed to use the adjoint modes of the Dirac operator for this purpose. In this talk we analyse an implementation of this idea that associates two Weyl fermionic modes in the adjoint representation to every gauge field configuration. The densities of these modes provide a filtered image of the self-dual and anti self-dual parts of the gauge action density. We present successful tests on the performance of this proposal on a set of initial gauge field configurations.