Topological data analysis of the deconfinement transition in SU(3) lattice gauge theory

TL;DR

This paper applies topological data analysis to SU(3) lattice gauge theory to uncover structural differences in phase transitions, revealing dualities and geometric features associated with confinement and deconfinement.

Contribution

It introduces a novel application of topological data analysis to SU(3) gauge theory, highlighting its ability to distinguish phase transition types and identify underlying topological structures.

Findings

Betti curves reveal electromagnetic dualities.

Plaquette susceptibilities correlate with geometric features.

Differences between first and second order phase transitions are identified.

Abstract

We study the confining and deconfining phases of pure $\mathrm{SU}(3)$ lattice gauge theory with topological data analysis. This provides unique insights into long range correlations of field configurations across the confinement-deconfinement transition. Specifically, we analyze non-trivial structures in electric and magnetic field energy densities as well as Polyakov loop traces and a Polyakov loop-based variant of the topological density. The Betti curves for filtrations based on the electric and magnetic field energy densities reveal signals of electromagnetic dualities. These dualities can be associated with an interchange in the roles of local lumps of electric and magnetic energy densities around the phase transition. Moreover, we show that plaquette susceptibilities can manifest in the geometric features captured by the Betti curves. We also compare these findings against earlier results for $\mathrm{SU}(2)$ and elaborate on the significant differences. Our results demonstrate that topological data analysis can identify clear differences between phase transitions of first and second order for non-Abelian lattice gauge theories and provides unprecedented insights into the relevant structures in their vicinity.