Particle theory

Abstract:

We perform lattice calculations of the spatial 't Hooft k-string tensions, σ̃k, 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 >> Tc our results match on to the known perturbative result, which exhibits Casimir Scaling, σ̃k∝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 ∂σ̃k/∂T∝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 the 'wetting' of these k-walls at T ≃ Tc and the (almost inevitable) 'perfect wetting' of the k ≤ N/2 domain wall. Our calculations show that as T→Tc the magnitude of σ̃k(T) decreases rapidly. This suggests the existence of a (would-be) 't Hooft string condensation transition at some temperature T H̃ 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 TH that is close to but above Tc. © SISSA 2005.