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Abstract:

We calculate bulk thermodynamic properties, such as the pressure, energy density, and entropy, in SU(4) and SU(8) lattice gauge theories, for the range of temperatures T≤2.0Tc and T≤1.6Tc, respectively. We find that the N=4,8 results are very close to each other, and to what one finds in SU(3), and are far from the asymptotic free-gas value. We conclude that any explanation of the high-T pressure (or entropy) deficit must be such as to survive the N→∞ limit. We give some examples of this constraint in action and comment on what this implies for the relevance of gravity duals. © 2005 Elsevier B.V. All rights reserved.

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 ��̃ 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.

Abstract:

We calculate the topological charge density of SU(N) lattice gauge fields for values of N up to N = 8 . The calculations are performed mostly at a fixed lattice spacing, a ≃ 1/5Tc, at which most other physical quantities show small lattice spacing corrections. Our T ≃ 0 topological susceptibility appears to approach a finite non-zero limit at N = ∞ that is consistent with earlier extrapolations from smaller values of N. Near the deconfining temperature Tc, we are able to investigate separately the confined and deconfined phases, since the transition is quite strongly first order. We find that the topological susceptibility in the confined phase is very similar at all T to that at T = 0 . By contrast, in the deconfined vacuum at larger N there are no topological fluctuations except for rare, isolated and small instantons. This shows that as N → ∞ the large-T suppression of large instantons and the large-N suppression of small instantons overlap, even at T ≃ Tc, so as to suppress a l l topological fluctuations in the deconfined phase. In the confined phase by contrast, the size distribution is much the same at all T, becoming more peaked as N grows, suggesting that perhaps D(ρ) α δ(rho; - ρc) at N = ∞, with ρc ∼ 1/Tc. © 2005 Elsevier B.V. All rights reserved.