Deconfinement transition and string tensions in SU(4) Yang-Mills theory

Abstract

We present results from numerical lattice calculations of SU(4) Yang-Mills theory. This work has two goals: to determine the order of the finite temperature deconfinement transition on an ${N}_{t}=6$ lattice and to study the string tensions between static charges in the irreducible representations of SU(4). Motivated by the argument of Pisarski and Tytgat that a second-order SU(\ensuremath{\infty}) deconfinement transition would explain some features of the SU(3) and QCD transitions, we confirm older results on a coarser, ${N}_{t}=4,$ lattice. We see a clear two-phase coexistence signal in the order parameter, characteristic of a first-order transition, at ${8/g}^{2}=10.79$ on a $6\ifmmode\times\else\texttimes\fi{}{20}^{3}$ lattice, on which we also compute a latent heat of $\ensuremath{\Delta}\ensuremath{\epsilon}\ensuremath{\approx}0.6{\ensuremath{\epsilon}}_{\mathrm{SB}}.$ Computing Polyakov loop correlation functions, we calculate the string tension at finite temperature in the confined phase between fundamental charges ${\ensuremath{\sigma}}_{1},$ between diquark charges ${\ensuremath{\sigma}}_{2},$ and between adjoint charges ${\ensuremath{\sigma}}_{4}.$ We find that $1<{\ensuremath{\sigma}}_{2}/{\ensuremath{\sigma}}_{1}<2,$ and our result for the adjoint string tension ${\ensuremath{\sigma}}_{4}$ is consistent with string breaking.