SU(4) pure-gauge phase structure and string tensions

We present numerical evidence that the SU(4) pure-gauge dynamics has a finite-temperature first-order phase transition. For a $6\times {20}^3$ lattice, this transition occurs at the inverse-square coupling of $8\mathrm{/}{g}^2\sim 10.79$. Below this and above the known bulk phase transition at $8\mathrm{/}{g}^2\sim 10.2$ is a confined phase in which we find two different string tensions, one between the fundamental 4 and $4^{\ast }$ representations and the other between the self-dual diquark 6 representations. The ratio of these two is about 1.5. The correlation in the adjoint representation suggests no string forms between adjoint charges.