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 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(∞) 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/g²=10.79 on a 6×20³ lattice, on which we also compute a latent heat of Δɛ~0.6ɛ_SB. 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.