The Role of Temperature in a Dimensional Approach to QCD_3

TL;DR

This paper investigates how temperature influences three-dimensional QCD by using a dimensional interpolation approach, constructing an effective two-dimensional theory at small widths, and analyzing phase transitions and thermodynamics.

Contribution

It introduces a dimensional interpolating method to study temperature effects in QCD_3 and explicitly calculates the deconfinement transition and thermodynamic behaviors.

Findings

Deconfining phase transition is demonstrated at high temperature.

Effective 2D theory reproduces QCD_3 physics at small widths.

Critical temperature and its dependence on the width are estimated.

Abstract

We analyze the role played by temperature in QCD_3 by means of a dimensional interpolating approach. Pure gauge QCD_3 is defined on a strip of finite width L, which acts as an interpolating parameter between two and three dimensions. A two-dimensional effective theory can be constructed for small enough widths giving the same longitudinal physics as QCD_3. Explicit calculations of T-dependent QCD_3 observables can thus be performed. The generation of a deconfinig phase transition, absent in QCD_2, is proven through an exact calculation of the electric or Debye mass at high T. Low and high T behaviors of relevant thermodynamic functions are also worked out. An accurate estimate of the critical temperature is given and its evolution with L is studied in detail.