Universal Aspects of Deconfinement in 2+1 Dimensions

TL;DR

This paper explores the universal features of deconfinement transitions in 2+1 dimensional SU(N) gauge theories, linking them to 2D Potts models and their dualities, with implications for understanding confinement in QCD.

Contribution

It establishes a connection between deconfinement in 2+1D gauge theories and 2D Potts models, providing exact results for critical phenomena and dualities relevant to confinement mechanisms.

Findings

Exact critical couplings and exponents for q<=4 Potts models

Duality between vortices and electric fluxes in 2D models

Relevance of center symmetry for confinement in QCD

Abstract

The 2+1 dimensional pure SU(N) gauge theories with N <= 4 are candidates for applying the powerful tools of scaling and universality to their deconfinement transitions at finite temperature. The corresponding 2 dimensional q-state Potts models with q <= 4 have 2nd order transitions, and we can exploit many exact results to obtain accurate critical couplings, transition temperatures, critical exponents, and the leading behavior of the continuum string tension near the phase transition on one side, together with its dual on the other. Thereby, the self-duality of the 2d spin models is reflected in a duality between spacelike vortices and confining electric fluxes. We also discuss the relevance of center symmetry and the corresponding vortices for confinement in full QCD when the electromagnetic interactions of fractionally charged quarks are included.