On the Nature of the Phase Transition in SU(N), Sp(2) and E(7) Yang-Mills theory

TL;DR

This paper investigates the nature of the confinement phase transition in various non-abelian gauge theories, finding predominantly first-order transitions with differences in strength explained by eigenvalue distributions.

Contribution

It provides a unified analysis of phase transition order in SU(N), Sp(2), and E(7) Yang-Mills theories using correlation functions and order-parameter potentials.

Findings

SU(N) with N=3,...,12 exhibits first-order transition

Sp(2) shows a first-order transition consistent with expectations

E(7) Yang-Mills also has a first-order transition, weaker than SU(N)

Abstract

We study the nature of the confinement phase transition in d=3+1 dimensions in various non-abelian gauge theories with the approach put forward in [1]. We compute an order-parameter potential associated with the Polyakov loop from the knowledge of full 2-point correlation functions. For SU(N) with N=3,...,12 and Sp(2) we find a first-order phase transition in agreement with general expectations. Moreover our study suggests that the phase transition in E(7) Yang-Mills theory also is of first order. We find that it is weaker than for SU(N). We show that this can be understood in terms of the eigenvalue distribution of the order parameter potential close to the phase transition.