Effective string description of the reconfined phase in the trace deformed $\mathrm{SU}(2)$ Yang-Mills theory in (2+1) dimensions

TL;DR

This paper investigates the flux tube behavior in the reconfined phase of a trace deformed SU(2) Yang-Mills theory in 2+1 dimensions, revealing agreement with a rigid string model through numerical simulations.

Contribution

It demonstrates that the flux tube in this phase aligns with the predictions of the rigid string model, highlighting the role of extrinsic curvature in the confining potential.

Findings

Flux tube behavior matches rigid string predictions

Reconfined phase exhibits vanishing Polyakov loop expectation value

Confining potential differs from usual gauge models

Abstract

We study the behaviour of the flux tube in the reconfined phase of the trace deformed $\mathrm{SU}(2)$ Yang-Mills theory in (2 + 1) dimensions. In this phase the Polyakov loop has a vanishing expectation value (and center symmetry is recovered) even at high temperatures. We study, by means of numerical simulations, the confining potential between two Polyakov loops. We show that its behaviour is very different from that of usual confining gauge models and shows a remarkable agreement with the predictions of the so called "rigid string" in the limit in which the rigidity term (i.e. a term proportional to the square of the extrinsic curvature of the string) is very large and is the dominant contribution in the action.