The Deconfinement Phase Transition of Sp(2) and Sp(3) Yang-Mills Theories in 2+1 and 3+1 Dimensions

TL;DR

This study investigates the nature of the deconfinement phase transition in Sp(2) and Sp(3) Yang-Mills theories across 2+1 and 3+1 dimensions, revealing how gauge group size influences transition order.

Contribution

It provides the first lattice simulation analysis of Sp(N) Yang-Mills theories, demonstrating the impact of gauge group size on the order of the deconfinement transition.

Findings

Sp(2) in 3+1 dimensions exhibits a first order transition.

Sp(2) in 2+1 dimensions shows a second order transition with Ising universality.

Sp(3) has a first order transition in both dimensions.

Abstract

Some time ago, 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 spin model symmetric under the center of G. For d=3 these arguments have been confirmed numerically only in the SU(2) case with center Z(2), simply because all SU(N) Yang-Mills theories with N>=3 seem to have non-universal first order phase transitions. The symplectic groups Sp(N) also have the center Z(2) and provide another extension of SU(2) = Sp(1) to general N. Using lattice simulations, we find that the deconfinement phase transition of Sp(2) Yang-Mills theory is first order in 3+1 dimensions, while in 2+1 dimensions stronger fluctuations induce a second order transition. In agreement with the Svetitsky-Yaffe conjecture, for (2+1)-d Sp(2) Yang-Mills theory we find the universal critical behavior of the 2-d Ising model. For Sp(3) Yang-Mills theory the transition is first order both in 2+1 and in 3+1 dimensions. This suggests that the size of the gauge group -- and not the center symmetry -- determines the order of the deconfinement phase transition.