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 Pisarski and Tytgat's argument that a second-order SU($\infty$) 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, characteristic of a first-order transition, at $8/g^2 = 10.79$ on a $6\times 20^3$ lattice, on which we also compute a latent heat of $Δε\approx 0.6 ε_{SB}$. Computing Polyakov loop correlation functions we calculate the string tension at finite temperature in the confined phase between fundamental charges, $σ_1$, between diquark charges, $σ_2$, and between adjoint charges $σ_4$. We find that $1 < σ_2/σ_1 < 2$, and our result for the adjoint string tension $σ_4$ is consistent with string breaking.