The Zero Temperature Chiral Phase Transition in SU(N) Gauge Theories

We investigate the zero temperature chiral phase transition in an SU(N) gauge theory as the number of fermions $N_f$ is varied. We argue that there exists a critical number of fermions $N_f^c$, above which there is no chiral symmetry breaking or confinement, and below which both chiral symmetry breaking and confinement set in. We estimate $N_f^c$ and discuss the nature of the phase transition.Comment: 13 pages, LaTeX, version published in PR

Phase Structure of Non-Compact QED3 and the Abelian Higgs Model

We review the phase structure of a three-dimensional, non-compact Abelian gauge theory (QED3) as a function of the number $N$ of 4-component massless fermions. There is a critical $N_{c}$ up to which there is dynamical fermion mass generation and an associated global symmetry breaking. We discuss various approaches to the determination of $N_c$, which lead to estimates ranging from $N_c =1$ to $N_c =4$. This theory with N=2 has been employed as an effective continuum theory for the 2D quantum antiferromagnet where the observed Neel ordering corresponds to dynamical fermion mass generation. Thus the value of $N_c$ is of some physical interest. We also consider the phase structure of the model with a finite gauge boson mass (the Abelian Higgs model).Comment: 14 pages, corrected the normalization of the fermion condensate in section V, corrected a typo in the reference

2+1 Dimensional QED and a Novel Phase Transition

We investigate the chiral phase transition in 2+1 dimensional QED. Previous gap equation and lattice Monte-Carlo studies of symmetry breaking have found that symmetry breaking ceases to occur when the number of fermion flavors exceeds a critical value. Here we focus on the order of the transition. We find that there are no light scalar degrees of freedom present as the critical number of flavors is approached from above (in the symmetric phase). Thus the phase transition is not second order, rendering irrelevant the renormalization group arguments for a fluctuation induced transition. However, the order parameter vanishes continuously in the broken phase, so this transition is also unlike a conventional first order phase transition.Comment: 11 pages, Late

Postmodern Technicolor

Using new insights into strongly coupled gauge theories arising from analytic calculations and lattice simulations, we explore a framework for technicolor model building that relies on a non-trivial infrared fixed point, and an essential role for QCD. Interestingly, the models lead to a simple relation between the electroweak scale and the QCD confinement scale, and to the possible existence of exotic leptoquarks with masses of several hundred GeV.Comment: LaTeX, 13 pages, version published in PR

The Phase Structure of an SU(N) Gauge Theory with N_f Flavors

We investigate the chiral phase transition in SU(N) gauge theories as the number of quark flavors, $N_f$, is varied. We argue that the transition takes place at a large enough value of $N_f$ so that it is governed by the infrared fixed point of the $\beta$ function. We study the nature of the phase transition analytically and numerically, and discuss the spectrum of the theory as the critical value of $N_f$ is approached in both the symmetric and broken phases. Since the transition is governed by a conformal fixed point, there are no light excitations on the symmetric side. We extend previous work to include higher order effects by developing a renormalization group estimate of the critical coupling.Comment: 34 pages, 1 figure. More references adde

A Comment on the Zero Temperature Chiral Phase Transition in SU(N)SU(N) Gauge Theories

Recently Appelquist, Terning, and Wijewardhana investigated the zero temperature chiral phase transition in SU(N) gauge theory as the number of fermions N_f is varied. They argued that there is a critical number of fermions N^c_f, above which there is no chiral symmetry breaking and below which chiral symmetry breaking and confinement set in. They further argued that that the transition is not second order even though the order parameter for chiral symmetry breaking vanishes continuously as N_f approaches N^c_f on the broken side. In this note I propose a simple physical picture for the spectrum of states as N_f approaches N^c_f from below (i.e. on the broken side) and argue that this picture predicts very different and non-universal behavior than is the case in an ordinary second order phase transition. In this way the transition can be continuous without behaving conventionally. I further argue that this feature results from the (presumed) existence of an infrared Banks-Zaks fixed point of the gauge coupling in the neighborhood of the chiral transition and therefore depends on the long-distance nature of the non-abelian gauge force.Comment: 7 pages, 2 figure

Zero Temperature Chiral Phase Transition in (2+1)-Dimensional QED with a Chern-Simons Term

We investigate the zero temperature chiral phase transition in (2+1)-dimensional QED in the presence of a Chern-Simons term, changing the number of fermion flavors. In the symmetric phase, there are no light degrees of freedom even at the critical point. Unlike the case without a Chern-Simons term, the phase transition is first-order.Comment: 7 pages, RevTeX, no figure

Fermion Masses and Mixing in Extended Technicolor Models

We study fermion masses and mixing angles, including the generation of a seesaw mechanism for the neutrinos, in extended technicolor (ETC) theories. We formulate an approach to these problems that relies on assigning right-handed $Q=-1/3$ quarks and charged leptons to ETC representations that are conjugates of those of the corresponding left-handed fermions. This leads to a natural suppression of these masses relative to the $Q=2/3$ quarks, as well as the generation of quark mixing angles, both long-standing challenges for ETC theories. Standard-model-singlet neutrinos are assigned to ETC representations that provide a similar suppression of neutrino Dirac masses, as well as the possibility of a realistic seesaw mechanism with no mass scale above the highest ETC scale of roughly $10^3$ TeV. A simple model based on the ETC group SU(5) is constructed and analyzed. This model leads to non-trivial, but not realistic mixing angles in the quark and lepton sectors. It can also produce sufficiently light neutrinos, although not simultaneously with a realistic quark spectrum. We discuss several aspects of the phenomenology of this class of models.Comment: 74 pages, revtex with embedded figure

Phases of Chiral Gauge Theories

We discuss the behavior of two non-supersymmetric chiral SU(N) gauge theories, involving fermions in the symmetric and antisymmetric two-index tensor representations respectively. In addition to global anomaly matching, we employ a recently proposed inequality constraint on the number of effective low energy (massless) degrees of freedom of a theory, based on the thermodynamic free energy. Several possible zero temperature phases are consistent with the constraints. A simple picture for the phase structure emerges if these theories choose the phase, consistent with global anomaly matching, that minimizes the massless degree of freedom count defined through the free energy. This idea suggests that confinement with the preservation of the global symmetries through the formation of massless composite fermions is in general not preferred. While our discussion is restricted mainly to bilinear condensate formation, higher dimensional condensates are considered for one case. We conclude by commenting briefly on two related supersymmetric chiral theories.Comment: 23 pages, 2 figures, ReVTeX, improved forma

Trouble for MAC

We show that the next-to-leading corrections to the kernel of the gap equation can be large and of opposite sign to the lowest order kernel, in the presence of a gauge boson mass. This calls into question the reliability of the Most Attractive Channel hypothesis.Comment: 8 pages, 1 figure, LaTe