Deconfinement in Yang-Mills: a conjecture for a general gauge Lie group G

TL;DR

This paper investigates the nature of deconfinement phase transitions in various Yang-Mills theories with different gauge groups, using lattice simulations to explore the universality class and conjecture about the transition order across these groups.

Contribution

It extends the study of deconfinement transitions beyond SU(N) to include Sp(N) and exceptional groups, proposing a general conjecture on transition order for various gauge groups.

Findings

Sp(2) and Sp(3) Yang-Mills theories show different transition orders in (2+1)d and (3+1)d.

Numerical results support the conjecture relating gauge group properties to transition order.

G(2) Yang-Mills theory exhibits a specific deconfinement transition behavior.

Abstract

Svetitsky and Yaffe have argued that -- if the deconfinement phase transition of a (d+1)-dimensional Yang-Mills theory with gauge group G is second order -- it should be in the universality class of a d-dimensional scalar model symmetric under the center C(G) of G. These arguments have been investigated numerically only considering Yang-Mills theory with gauge symmetry in the G=SU(N) branch, where C(G)=Z(N). The symplectic groups Sp(N) provide another extension of SU(2)=Sp(1) to general N and they all have the same center Z(2). Hence, in contrast to the SU(N) case, Sp(N) Yang-Mills theory allows to study the relevance of the group size on the order of the deconfinement phase transition keeping the available universality class fixed. Using lattice simulations, we present numerical results for the deconfinement phase transition in Sp(2) and Sp(3) Yang-Mills theories both in (2+1)d and (3+1)d. We then make a conjecture on the order of the deconfinement phase transition in Yang-Mills theories with general Lie groups SU(N), SO(N), Sp(N) and with exceptional groups G(2), F(4), E(6), E(7), E(8). Numerical results for G(2) Yang-Mills theory at finite temperature in (3+1)d are also presented.