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

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.

arXiv comment10 pages, 10 figures

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• Different faces of confinement
• Localization properties of Dirac modes at the Roberge-Weiss phase transition
• Localization of Dirac modes in finite-temperature ${\mathbb{Z}}_2$ gauge theory on the lattice
• Localised Dirac eigenmodes, chiral symmetry breaking, and Goldstone's theorem at finite temperature
• Deconfinement transition and localization of Dirac modes in finite-temperature ${\mathbb{Z}}_3$ gauge theory on the lattice
• Localisation of Dirac modes in gauge theories and Goldstone's theorem at finite temperature
• Localisation of Dirac eigenmodes and confinement in gauge theories: the Roberge-Weiss transition