Dr Michael Teper

Abstract:

I review some of the things we have learned about large N gauge theories (and QCD∞) from lattice calculations in recent years. I point to some open problems.

Abstract:

We calculate the excitation spectrum of closed k-strings in 2+1 dimensional SU(N) gauge theories for N = 4, 5 and k = 2. Our results demonstrate that the low-lying spectrum of the k = 2 string falls into sectors that belong to nearly pure antisymmetric and symmetric representations, showing that k-strings know not only about the centre of the group, but also about the full group. We also observe that the lightest states in each irreducible representation are consistent with what one would expect from an effective string theory that belongs to the same bosonic universality class (Nambu-Goto) as the fundamental string. We find that the corrections compared to the free string theory are of O(1), in striking contrast to the very small correction observed for the fundamental string. We also observe unbound w = 2 states.

Abstract:

We use lattice techniques to study the closed-string spectrum of SU (N) gauge theories in 2 + 1 dimensions. We calculate the energies of the lowest lying ∼30 states for strings with lengths between l ∼ 0.45  fm and l ∼ 3  fm, and compare to different theoretical predictions. We obtain unambiguous evidence that the closed-strings are in the universality class of the Nambu-Goto free bosonic string. Moreover, we clearly see that our data can be described by a covariant string theory with a small/moderate correction down to very short distance scales, and possibly on all distance scales at large-N. © 2007 Elsevier B.V. All rights reserved.

Abstract:

We present numerical evidence for the spontaneous breaking of the ZN⁴ symmetry of four-dimensional twisted Eguchi-Kawai models with SU(N) gauge group and symmetric twist, for sufficiently large N. We find that for N ≥ 100 this occurs for a wide range of bare couplings. Moreover for N ≤ 144, where we have been able to perform detailed calculations, there is no window of couplings where the physically interesting confined and deconfined phases appear in the reduced model. We provide a possible interpretation for this in terms of generalised 'fluxon' configurations. We discuss the implications of our findings for the validity and utility of space-time reduced models as N → ∞. © 2007 Elsevier B.V. All rights reserved.

Abstract:

We use lattice techniques to calculate the continuum string tensions of SU (N) gauge theories in 2 + 1 dimensions. We attempt to control all systematic errors at a level that allows us to perform a precise test of the analytic prediction of Karabali, Kim and Nair. We find that their prediction is within 3% of our values for all N and that the discrepancy decreases with increasing N. When we extrapolate our results to N = ∞ we find that there remains a discrepancy of ≃ 1 %, which is a convincing ∼ 6 σ effect. Thus, while the Karabali-Nair analysis is remarkably accurate at N = ∞, it is not exact. © 2006 Elsevier B.V. All rights reserved.