ZN domain walls in hot N=4 SYM at weak and strong coupling

We study the tensions of domain walls in the deconfined phase of N = 4 SUSY Yang-Mills theory on R-3 x S-1, at weak and strong coupling. We calculate the k-wall tension at one-loop order and find that it is proportional to k(N - k) (Casimir scaling). The two-loops analysis suggests that Casimir scaling persists to this order. The strong coupling calculation is performed by using the AdS/CFT correspondence. We argue that the k-wall should be identified with an NS5-brane wrapping an S-4 inside S-5 in the AdS-Schwarzschild X S-5 background in Type IIB string theory. The tension at strong coupling is compared with the weak coupling result. We also compare our results with those from lattice simulations in pure Yang-Mills theory.