Dr Michael Teper

Abstract:

We extend our earlier investigation of the finite temperature deconfinement transition in SU(N) gauge theories, with the emphasis on what happens as N → ∞. We calculate the latent heat, Lh, in the continuum limit, and find the expected behaviour, Lh ∝ N², at large N. We confirm that the phase transition, which is second order for SU(2) and weakly first order for SU(3), becomes robustly first order for N ≥ 4 and strengthens as N increases. As an aside, we explain why the SU(2) specific heat shows no sign of any peak as T is varied across what is supposedly a second order phase transition. We calculate the effective string tension and electric gluon masses at T ≃ Tc confirming the discontinuous nature of the transition for N ≥ 3. We explicitly show that the large-N 'spatial' string tension does not vary with T for T ≤ Tc and that it is discontinuous at T = Tc. For T ≥ Tc it increases ∝ T² to a good approximation, and the k-string tension ratios closely satisfy Casimir Scaling. Within very small errors, we find a single T c at which all the k-strings deconfine, i.e. a step-by-step breaking of the relevant centre symmetry does not occur. We calculate the interface tension but are unable to distinguish between the ∝ N or ∝ N ² variations, each of which can lead to a striking but different N = ∞ deconfinement scenario. We remark on the location of the bulk phase transition, which bounds the range of our large-N calculations on the strong coupling side, and within whose hysteresis some of our larger-N calculations are performed. © SISSA/ISAS 2005.

Abstract:

We calculate in the SU(6) gauge theory the mass of the lightest flux loop that winds around a spatial torus, as a function of the torus size, taking care to achieve control of the main systematic errors. For comparison we perform a similar calculation in SU(4). We demonstrate approximate linear confinement and show that the leading correction is consistent with what one expects if the flux tube behaves like a simple bosonic string at long distances. We obtain similar but less accurate results for stable (k-)strings in higher representations. We find some evidence that for k > 1 the length scale at which the bosonic string correction becomes dominant increases as N increases. We perform all these calculations not just for long strings, up to about 2.5'fm' in length, but also for shorter strings, down to the minimum length, lc = 1/T c, where Tc is the deconfining temperature. We find that the mass of the ground-state string, at all length scales, is not very far from the simple Nambu-Goto string theory prediction, and that the fit improves as N increases from N = 4 to N = 6. We estimate the mass of the first excited string and find that it also follows the Nambu-Goto prediction, albeit more qualitatively. We comment upon the significance of these results for the string description of SU(N) gauge theories in the limit N = ∞. © SISSA/ISAS 2005.