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

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