  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 $\Delta\epsilon\approx 0.6 \epsilon_{SB}$. Computing
Polyakov loop correlation functions we calculate the string tension at finite
temperature in the confined phase between fundamental charges, $\sigma_1$,
between diquark charges, $\sigma_2$, and between adjoint charges $\sigma_4$. We
find that $1 < \sigma_2/\sigma_1 < 2$, and our result for the adjoint string
tension $\sigma_4$ is consistent with string breaking.
