Dr Michael Teper

Abstract:

We perform an exploratory investigation of how rapidly the physics of SO(2N) gauge theories approaches its N = ∞ limit. This question has recently become topical because SO(2N) gauge theories are orbifold equivalent to SU(N) gauge theories, but do not have a finite chemical potential sign problem. It is therefore interesting to know how close is the physics of SO(N) to that of SU(3) for the modest values of N where one might be able to perform chemical potential calculations. We consider only the pure gauge theory and, because of the inconvenient location of the lattice strong-to-weak coupling 'bulk' transition in 3 + 1 dimensions, we largely confine our numerical calculations to 2 + 1 dimensions in this paper. We provide some analytic estimates of the SO(2N) spectrum in both D = 2 + 1 and D = 3 + 1, and show, numerically, that the D = 2 + 1 SO(6) and SU(4) low-lying spectra do indeed appear to be the same. Our numerical calculations of a number of mass ratios show that the leading O(1/N) correction already dominates for N ≥ 6, and in some cases down to N = 4, and that, as expected, these ratios become consistent with those of SU(N) as N → ∞. In particular we see that SO(6) and SU(3) gauge theories are quite similar except for the values of the string tension and coupling, both of which differences can be readily understood. © 2013 SISSA, Trieste, Italy.

Abstract:

We investigate the low-lying spectrum of closed confining flux-tubes that wind around a spatial torus in D = 2+1 and carry flux in different representations of SU(N). We focus on our most recent calculations for N = 6 and β?= 171, where the calculated low-energy physics is very close to the continuum and large-N limits. We investigate the adjoint, 84, 120, k = 2A, 2S and k = 3A, 3M, 3S representations and show that the corresponding flux-tubes do exist. Similarly to the results for the fundamental representation, the ground state of a flux-tube with momentum along its axis appears to be well described by Nambu-Goto all the way down to very short tubes. In contrast, excited states have much larger deviations from Nambu-Goto. We discuss whether these states are non-string-like and associated with excitations of massive flux-tube modes.

Abstract:

We identify and characterise the conformal window in gauge theories relevant for beyond the standard model building, e.g. technicolour, using the criteria of metric confinement and causal analytic couplings, which are known to be consistent with the phase diagram of supersymmetric QCD from Seiberg duality. Using these criteria we find perturbation theory to be consistent throughout the predicted conformal window for several of these gauge theories and we discuss recent lattice results in the light of our findings. © 2010 Elsevier B.V.

Abstract:

We calculate the energy spectrum of a confining flux tube that is closed around a spatial torus, as a function of its length ℓ. We do so for various SU(N) gauge theories in 3+1 dimensions, and for various values of spin, parity and longitudinal momentum. We are able to present usefully accurate results for about 20 of the lightest such states, for a range of ℓ that begins close to the (finite volume) deconfining phase transition at ℓ √σ ∼ 1.6, and extends up to ℓ√σ ∼ 6 (where σ is the string tension). We find that most of these low-lying states are well described by the spectrum of the Nambu-Goto free string theory in flat space-time. Remarkably, this is so not only at the larger values of ℓ, where the gap between the ground state energy and the low-lying excitations becomes small compared to the mass gap, but also down to much shorter lengths where these excitation energies become large compared to √σ, the flux-tube no longer 'looks' anything like a thin string, and an expansion of the effective string action in powers of 1/ℓ no longer converges. All this is for flux in the fundamental representation. We also calculate the k = 2 (anti)symmetric ground states and these show larger corrections at small ℓ. So far all this closely resembles our earlier findings in 2+1 dimensions. However, and in contrast to the situation in D = 2+1, we also find that there are some states, with J = 0 quantum numbers, that show large deviations from the Nambu-Goto spectrum. We investigate the possibility that (some of) these states may encode the massive modes associated with the internal structure of the flux tube, and we discuss how the precocious free string behaviour of most states constrains the effective string action, on which much interesting theoretical progress has recently been made.