The deconfinement phase transition of Sp(2) and Sp(3) Yang–Mills theories in 2+1 and 3+1 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 2d 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.