Confining Flux Tube in the Trace Deformed (2+1) Dimensional SU(2) Gauge Theory

Abstract

We study the confining flux tube in the reconfined phase of trace deformed SU(2) Yang-Mills theory in (2+1) dimensions. Using lattice simulations above the standard deconfinement temperature, we analyze Polyakov-loop correlators and extract the ground state energy of the effective string. We show that the usual Nambu-Goto effective string description, including its standard higher-order corrections, fails to reproduce the data as the trace deformation is increased. Remarkably, deep in the reconfined regime the results are instead accurately described by the Polchinski-Yang rigid-string solution, corresponding to an effective string dominated by an extrinsic-curvature term. We further investigate the transverse profile of the chromo-electric flux tube and find significant deviations from the standard Yang-Mills behavior, including a substantial modification of the intrinsic width. Finally, we present an exploratory study of the phase diagram, finding evidence for a transition from a continuous to a first order reconfinement line as the deformation parameter increases. These results suggest that the reconfined phase realizes a qualitatively different effective-string regime from ordinary confinement.