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

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 Nt = 6 lattice and to study the string tensions between static charges in the irreducible representations of SU(4). Motivated by Pisarski and Tytgat’s argument that a second-order SU(∞) deconfinement transition would explain some features of the SU(3) and QCD transitions, we confirm older results on a coarser, Nt = 4, lattice. We see a clear two-phase coexistence signal in the order parameter, characteristic of a first-order transition, at 8/g = 10.79 on a 6 × 20 lattice, on which we also compute a latent heat of ∆ǫ ≈ 0.6ǫSB. Computing Polyakov loop correlation functions we calculate the string tension at finite temperature in the confined phase between fundamental charges, σ1, between diquark charges, σ2, and between adjoint charges σ4. We find that 1 < σ2/σ1 < 2, and our result for the adjoint string tension σ4 is consistent with string breaking.