Large Nc physics from the lattice

I summarise what lattice methods can contribute to our understanding of the phenomenology of QCD at large Nc and describe some recent work on the physics of SU(Nc) gauge theories. These non-perturbative calculations show that there is indeed a smooth Nc -> infinity limit and that it is achieved by keeping g.g.Nc fixed, confirming the usual diagrammatic analysis. The lattice calculations support the crucial assumption that the theory remains linearly confining at large Nc. Moreover we see explicitly that Nc=3 is `close to' Nc=infinity for many physical quantities. We comment on the fate of topology and the deconfining transition at large Nc. We find that multiple confining strings are strongly bound. The string tensions, K(k), of these k-strings are close to the M(-theory)QCD-inspired conjecture as well as to `Casimir scaling' with the most accurate recent calculations favouring the former. We point out that closed k-strings provide a natural way for non-perturbative effects to introduce O(1/Nc) corrections into the pure gauge theory, in contradiction to the conventional diagrammatic expectation.Comment: 10 pages. Invited talk, The Phenomenology of Large-Nc QCD, to be published Proceedings of the Institute of Nuclear Theor

The topological susceptibility in `full' (UK)QCD

We report first calculations of the topological susceptibility measured using the field theoretic method on SU(3) gauge configurations produced by the UKQCD collaboration with two flavours of dynamical, improved, Wilson fermions. Using three ensembles with matched lattice spacing but differing sea quark mass we find that hybrid Monte Carlo simulation appears to explore the topological sectors efficiently, and a topological susceptibility consistent with increasing linearly with the quark mass.Comment: LaTeX. 4 PostScript figures. Contribution to LATTICE99(topology

On the relation between the width of the flux tube and Tc−1T_c^{-1} in lattice gauge theories

Within the framework of a quantum flux tube model for the interquark potential it is possible to predict that in (2+1) dimensions the space-like string tension must increase with the temperature in the deconfined phase and that the thickness of the flux tube must coincide with the inverse of the deconfinement temperature. Both these predictions are in good agreement with some recent numerical simulations of SU(2) and $Z_2$ gauge models.Comment: 3 pages, uuencoded .ps file (Proceeding of Lattice '93 Conference

Topology in CP(N-1) models: a critical comparison of different cooling techniques

Various cooling methods, including a recently introduced one which smoothes out only quantum fluctuations larger than a given threshold, are applied to the study of topology in 2d CP(N-1) models. A critical comparison of their properties is performed.Comment: Poster at LATTICE99(Topology and confinement), 3 pages, 5 eps figures, uses espcrc2.st

Thermodynamics of the QCD plasma and the large-N limit

The equilibrium thermodynamic properties of the SU(N) plasma at finite temperature are studied non-perturbatively in the large-N limit, via lattice simulations. We present high-precision numerical results for the pressure, trace of the energy-momentum tensor, energy density and entropy density of SU(N) Yang-Mills theories with N=3, 4, 5, 6 and 8 colors, in a temperature range from 0.8T_c to 3.4T_c (where T_c denotes the critical deconfinement temperature). The results, normalized according to the number of gluons, show a very mild dependence on N, supporting the idea that the dynamics of the strongly-interacting QCD plasma could admit a description based on large-N models. We compare our numerical data with general expectations about the thermal behavior of the deconfined gluon plasma and with various theoretical descriptions, including, in particular, the improved holographic QCD model recently proposed by Kiritsis and collaborators. We also comment on the relevance of an AdS/CFT description for the QCD plasma in a phenomenologically interesting temperature range where the system, while still strongly-coupled, approaches a `quasi-conformal' regime characterized by approximate scale invariance. Finally, we perform an extrapolation of our results to the N to $\infty$ limit.Comment: 1+38 pages, 13 eps figures; v2: added reference

3-D lattice simulation of the electroweak phase transition at small Higgs mass

We study the electroweak phase transition by lattice simulations of an effective 3-dimensional theory, for a Higgs mass of about $35 GeV$. In the broken symmetry phase our results on masses and the Higgs condensate are consistent with 2-loop perturbative results. However, we find a non-perturbative lowering of the transition temperature, similar to the one previously found at $m_H = 80 GeV$. For the symmetric phase, bound state masses and the static force are determined and compared with results for pure $SU(2)$ theory.Comment: 11 pages, uuencoded ps-file, 5 postscript figures include