Dr Michael Teper

Abstract:

We calculate energies and tensions of closed k-strings in (2+1)-dimensional SU(N) gauge theories with N=4,5,6,8. When we study the dependence of the ground state energy on the string length, we find that it is well described by a Nambu-Goto (NG) free bosonic string for large lengths. At shorter lengths we see deviations which we fit, and this allows us to control the systematic error involved in extracting the tension. We compare the resulting string tensions with Casimir scaling, which we find to be lower than our data by 1% − 4%. Extrapolating our results to N = ∞ we see that our data fits more naturally to 1/N rather than 1/N 2 corrections. Finally, we see that the full spectrum of the k-string states falls into sectors that belong to particular irreducible representations of SU (N).

Abstract:

We investigate numerically the phase structure of the Twisted Eguchi-Kawai (TEK) model in four dimensions. In the numerical simulations of the zero-temperature TEK model (using a symmetric twist) we observe the existence of new phases that break its ZN4 symmetry at intermediate lattice couplings and for large SU(N) gauge groups. This effect can be explained by the contribution of diagonal configurations with collapsed eigenvalues, which are particular cases of “generalised fluxons”. We also investigate finite-temperature versions of the TEK model using anisotropic lattice couplings, where in particular we find van Baal fluxons contributing at large anisotropies.

Abstract:

For ☎ there is a first order bulk transition that cleanly separates the strong and weak coupling regimes of SU( ) lattice gauge theories with the plaquette action. We find that in this case the calculated string tension can be readily fitted throughout the weak coupling region by a standard 3-loop perturbative expression modified by lattice spacing corrections of the expected form. While our fits demand the presence of the latter, they are not constraining enough to tell us which of the various bare coupling schemes is a ‘good’ one, in the sense that terms in the -function beyond 3-loops are indeed negligible (in the relevant range of scales). To resolve this ambiguity we work in SU(3), using the Schrodinger Functional coupling scheme as a benchmark, and find that the Parisi mean-field improved coupling scheme matches it very well. Using the latter scheme, we have fitted the values of the string tension ✡ that have been calculated for ☎, to obtain ✡✚ ★ for , where the first error is statistical and the second is our estimate of the systematic error from all sources.

Abstract:

We study the closed-string spectrum of SU(N) gauge theories in the fundamental representation in 2+1 dimensions. We calculate the energies of the lowest lying ∼ 30 states using a large variety of operators characterised by the quantum numbers of parity and longitudinal momentum. We find that our results for the ground state are very well approximated by the Nambu-Goto (NG) predictions even for short strings. For the excited states, we observe significant deviations from the NG predictions only for very short strings and they decrease rapidly with increasing string length. Finally, we see that Nambu-Goto provides a much better description of our results than the effective string theoretical predictions. We discuss the continuum and large-N limits.

Abstract:

We find a strong-to-weak coupling crossover in D=2+1 SU(N) lattice gauge theories that appears to become a third-order phase transition at N=∞, in a similar way to the Gross-Witten transition in the D=1+1 SU(N→∞) lattice gauge theory. There is, in addition, a peak in the specific heat at approximately the same coupling that increases with N, which is connected to ZN monopoles (instantons), reminiscent of the first-order bulk transition that occurs in D=3+1 lattice gauge theories for N≥5. Our calculations are not precise enough to determine whether this peak is due to a second-order phase transition at N=∞ or to the third-order phase transition having a critical behavior different to that of the Gross-Witten transition. We show that as the lattice spacing is reduced, the N=∞ gauge theory on a finite 3-torus appears to undergo a sequence of first-order ZN symmetry breaking transitions associated with each of the tori (ordered by size). We discuss how these transitions can be understood in terms of a sequence of deconfining transitions on ever-more dimensionally reduced gauge theories. We investigate whether the trace of the Wilson loop has a nonanalyticity in the coupling at some critical area, but find no evidence for this. However we do find that, just as one can prove occurs in D=1+1, the eigenvalue density of a Wilson loop forms a gap at N=∞ at a critical value of its trace. We show that this gap formation is in fact a corollary of a remarkable similarity between the eigenvalue spectra of Wilson loops in D=1+1 and D=2+1 (and indeed D=3+1): for the same value of the trace, the eigenvalue spectra are nearly identical. This holds for finite as well as infinite N; irrespective of the Wilson loop size in lattice units; and for Polyakov as well as Wilson loops. © 2006 The American Physical Society.