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Abstract:

We show that under general conditions there is at least one natural inflationary direction for the Kahler moduli of type IIB flux compactifications. This requires a Calabi-Yau which has h^{2,1}>h^{1,1}>2 and for which the structure of the scalar potential is as in the recently found exponentially large volume compactifications. We also need - although these conditions may be relaxed - at least one Kahler modulus whose only non-vanishing triple-intersection is with itself and which appears by itself in the non-perturbative superpotential. Slow-roll inflation then occurs without a fine tuning of parameters, evading the eta problem of F-term inflation. In order to obtain COBE-normalised density perturbations, the stabilised volume of the Calabi-Yau must be O(10^5-10^7) in string units, and the inflationary scale M_{infl} ~ 10^{13} GeV. We find a robust model independent prediction for the spectral index of 1 - 2/N_e = 0.960 - 0.967, depending on the number of efoldings.

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.