The decay of unstable k-strings in SU(N) gauge theories at zero and finite temperature

TL;DR

This paper investigates the decay and stability of k-strings in SU(N) gauge theories at zero and finite temperature, revealing representation-dependent tensions and decay scales through theoretical analysis and conformal field theory correspondence.

Contribution

It introduces a method to evaluate critical exponents exactly and proposes a generalized Wilson loop to estimate unstable string decay scales.

Findings

Representation-dependent string tensions at T=0

Exact evaluation of critical exponents via conformal field theory

Proposal of a generalized Wilson loop for decay scale estimation

Abstract

Sources in higher representations of SU(N) gauge theory at T=0 couple with apparently stable strings with tensions depending on the specific representation rather than on its N-ality. Similarly at the deconfining temperature these sources carry their own representation-dependent critical exponents. It is pointed out that in some instances one can evaluate exactly these exponents by fully exploiting the correspondence between the 2+1 dimensional critical gauge theory and the 2d conformal field theory in the same universality class. The emerging functional form of the Polyakov-line correlators suggests a similar form for Wilson loops in higher representations which helps in understanding the behaviour of unstable strings at T=0. A generalised Wilson loop in which along part of its trajectory a source is converted in a gauge invariant way into higher representations with same N-ality could be used as a tool to estimate the decay scale of the unstable strings.