Persistent homology as a probe for center vortices and deconfinement in SU(2) lattice gauge theory

TL;DR

This paper applies persistent homology from Topological Data Analysis to detect topological structures like center vortices in SU(2) lattice gauge theory and explores their role in the confinement-deconfinement transition.

Contribution

It introduces a gauge-invariant method using persistent homology to identify vortices and analyzes their connection to deconfinement with machine learning techniques.

Findings

Persistent homology detects vortices in gauge configurations.

Vortex presence correlates with deconfinement transition.

Quantitative analysis supports vortices' role in confinement.

Abstract

Topological Data Analysis (TDA) is a field that leverages tools and ideas from algebraic topology to provide robust methods for analysing geometric and topological aspects of data. One of the principal tools of TDA, persistent homology, produces a quantitative description of how the connectivity and structure of data changes when viewed over a sequence of scales. We propose that this presents a means to directly probe topological objects in gauge theories. We present recent work on using persistent homology to detect center vortices in SU(2) lattice gauge theory configurations in a gauge-invariant manner. We introduce the basics of persistence, describe our construction, and demonstrate that the result is sensitive to vortices. Moreover we discuss how, with simple machine learning, one can use the resulting persistence to quantitatively analyse the deconfinement transition via finite-size scaling, providing evidence on the role of vortices in relation to confinement in Yang-Mills theories.