Reconfinement, localization and thermal monopoles in $SU(3)$ trace-deformed Yang-Mills theory

TL;DR

This study uses lattice simulations to analyze the reconfinement phase transition in trace deformed SU(3) Yang-Mills theory, revealing it is first-order and exploring monopole condensation and Dirac eigenmode localization.

Contribution

It demonstrates that the reconfinement transition in trace deformed SU(3) Yang-Mills is first-order and links monopole condensation with Dirac mode delocalization in this framework.

Findings

Reconfined phase transition is first-order.

Dirac eigenmodes show Anderson-like transition behavior.

Thermal monopoles condense at reconfinement despite decreased density.

Abstract

We study, by means of numerical lattice simulations, the properties of the reconfinement phase transition taking place in trace deformed $SU(3)$ Yang-Mills theory defined on $\mathbb{R}^3\times S^1$, in which center symmetry is recovered even for small compactification radii. We show, by means of a finite size scaling analysis, that the reconfinement phase transition is first-order, like the usual $SU(3)$ thermal phase transition. We then investigate two different physical phenomena, which are known to characterize the standard confinement/deconfinement phase transition, namely the condensation of thermal magnetic monopoles and the change in the localization properties of the eigenmodes of the Dirac operator. Regarding the latter, we show that the mobility edge signalling the Anderson-like transition in the Dirac spectrum vanishes as one enters the reconfined phase, as it happens in the standard confined phase. Thermal monopoles, instead, show a peculiar behavior: their density decreases going through reconfinement, at odds with the standard thermal theory; nonetheless, they condense at reconfinement, like at the usual confinement transition. The coincidence of monopole condensation and Dirac mode delocalization, even in a framework different from that of the standard confinement transition, suggests the existence of a strict link between them.