Finite Temperature Phase Diagrams of Gauge Theories

We discuss finite temperature phase diagrams of SU(N) gauge theory with massless fermions as a function of the number of fermion flavors. Inside the conformal window we find a phase boundary separating two different conformal phases. Below the conformal window we find different phase structures depending on if the beta function of the theory has a first or higher order zero at the lower boundary of the conformal window. We also outline how the associated behaviors will help in distinguishing different types of theories using lattice simulations.Comment: 5 pages, 5 figure

Strong to weak coupling transitions of SU(N) gauge theories in 2+1 dimensions

We investigate strong-to-weak coupling transitions in D=2+1 SU(N->oo) gauge theories, by simulating lattice theories with a Wilson plaquette action. We find that there is a strong-to-weak coupling cross-over in the lattice theory that appears to become a third-order phase transition at N=oo, in a manner that is essentially identical to the Gross-Witten transition in the D=1+1 SU(oo) lattice gauge theory. There is also evidence for a second order transition at N=oo at approximately the same coupling, which is connected with centre monopoles (instantons) and so analogues to the first order bulk transition that occurs in D=3+1 lattice gauge theories for N>4. We show that as the lattice spacing is reduced, the N=oo gauge theory on a finite 3-torus suffers a sequence of (apparently) 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 non-analyticity in the coupling at some critical area, but find no evidence for this although, just as in D=1+1,the eigenvalue density of a Wilson loop forms a gap at N=oo for a critical trace. The physical implications of this are unclear.The gap formation is a special case 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.Comment: 44 pages, 28 figures. Extensive changes and clarifications with new results on non-analyticities and eigenvalue spectra of Wilson loops. This version to be submitted for publicatio

Infinite N phase transitions in continuum Wilson loop operators

We define smoothed Wilson loop operators on a four dimensional lattice and check numerically that they have a finite and nontrivial continuum limit. The continuum operators maintain their character as unitary matrices and undergo a phase transition at infinite N reflected by the eigenvalue distribution closing a gap in its spectrum when the defining smooth loop is dilated from a small size to a large one. If this large N phase transition belongs to a solvable universality class one might be able to calculate analytically the string tension in terms of the perturbative Lambda-parameter. This would be achieved by matching instanton results for small loops to the relevant large-N-universal function which, in turn, would be matched for large loops to an effective string theory. Similarities between our findings and known analytical results in two dimensional space-time indicate that the phase transitions we found only affect the eigenvalue distribution, but the traces of finite powers of the Wilson loop operators stay smooth under scaling.Comment: 31 pages, 9 figures, typos and references corrected, minor clarifications adde

A precise determination of the psibar-psi anomalous dimension in conformal gauge theories

A strategy for computing the psibar-psi anomalous dimension at the fixed point in infrared-conformal gauge theories from lattice simulations is discussed. The method is based on the scaling of the spectral density of the Dirac operator or rather its integral, the mode number. It is relatively cheap, mainly for two reasons: (a) the mode number can be determined with quite high accuracy, (b) the psibar-psi anomalous dimension is extracted from a fit of several observables on the same set of configurations (no scaling in the Lagrangian parameters is needed). As an example the psibar-psi anomalous dimension has been computed in the SU(2) theory with 2 Dirac fermions in the adjoint representation of the gauge group, and has been found to be 0.371(20). In this particular case, the proposed strategy has proved to be very robust and effective.Comment: LaTeX, 16 pages, 3 PDF figures, [v3] minor cosmetic change

Phases of three dimensional large N QCD on a continuum torus

It is established by numerical means that continuum large N QCD defined on a three dimensional torus can exist in four different phases. They are (i) confined phase; (ii) deconfined phase; (iii) small box at zero temperature and (iv) small box at high temperatures.Comment: 11 pages, 6 figures, 1 tabl

Improved Lattice Spectroscopy of Minimal Walking Technicolor

We present a numerical study of spectroscopic observables in the SU(2) gauge theory with two adjoint fermions using improved source and sink operators. We compare in detail our improved results with previous determinations of masses that used point sources and sinks and we investigate possible systematic effects in both cases. Such comparison enables us to clearly assess the impact of a short temporal extent on the physical picture, and to investigate some effects due to the finite spatial box. While confirming the IR-conformal behaviour of the theory, our investigation shows that in order to make firm quantitative predictions, a better handle on finite size effects is needed.Comment: 33 pages, 30 figures, 18 table

SO(2N) and SU(N) gauge theories in 2+1 dimensions

We perform an exploratory investigation of how rapidly the physics of SO(2N) gauge theories approaches its N=oo 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. 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. We discuss analytic expectations in both D=2+1 and D=3+1, show that the SO(6) and SU(4) spectra do indeed appear to be the same, and show that a number of mass ratios do indeed appear to agree in the large-N limit. In particular 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.Comment: 27 pages, 9 figure

An ideal toy model for confining, walking and conformal gauge theories: the O(3) sigma model with theta-term

A toy model is proposed for four dimensional non-abelian gauge theories coupled to a large number of fermionic degrees of freedom. As the number of flavors is varied the gauge theory may be confining, walking or conformal. The toy model mimicking this feature is the two dimensional O(3) sigma model with a theta-term. For all theta the model is asymptotically free. For small theta the model is confining in the infra red, for theta = pi the model has a non-trivial infra red fixed point and consequently for theta slightly below pi the coupling walks. The first step in investigating the notoriously difficult systematic effects of the gauge theory in the toy model is to establish non-perturbatively that the theta parameter is actually a relevant coupling. This is done by showing that there exist quantities that are entirely given by the total topological charge and are well defined in the continuum limit and are non-zero, despite the fact that the topological susceptibility is divergent. More precisely it is established that the differences of connected correlation functions of the topological charge (the cumulants) are finite and non-zero and consequently there is only a single divergent parameter in Z(theta) but otherwise it is finite. This divergent constant can be removed by an appropriate counter term rendering the theory completely finite even at theta > 0.Comment: 9 pages, 2 figures, minor modification, references adde