Casimir scaling of domain wall tensions in the deconfined phase of D=3+1 SU(N) gauge theories

Abstract: We perform lattice calculations of the spatial 't Hooft k-string tensions in the deconfined phase of SU(N) gauge theories for N=2,3,4,6. These equal (up to a factor of T) the surface tensions of the domain walls between the corresponding (Euclidean) deconfined phases. For T much larger than Tc our results match on to the known perturbative result, which exhibits Casimir Scaling, being proportional to k(N-k). At lower T the coupling becomes stronger and, not surprisingly, our calculations show large deviations from the perturbative T-dependence. Despite this we find that the behaviour proportional to k(N-k) persists very accurately down to temperatures very close to Tc. Thus the Casimir Scaling of the 't Hooft tension appears to be a universal' feature that is more general than its appearance in the low order high-T perturbative calculation. We observe thewetting' of these k-walls at T around Tc and the (almost inevitable) perfect wetting' of the k=N/2 domain wall. Our calculations show that as T tends to Tc the magnitude of the spatialt Hooft string tension decreases rapidly. This suggests the existence of a (would-be) 't Hooft string condensation transition at some temperature which is close to but below Tc. We speculate on the `dual' relationship between this and the (would-be) confining string condensation at the Hagedorn temperature that is close to but above Tc.