The unphysical nature of the SL(2,R) symmetry and its associated condensates in Yang-Mills theories

BRST cohomology methods are used to explain the origin of the SL(2,R) symmetry in Yang-Mills theories. Clear evidence is provided for the unphysical nature of this symmetry. This is obtained from the analysis of a local functional of mass dimension two and constitutes a no-go statement for giving a physical meaning to condensates associated with the symmetry breaking of SL(2,R).Comment: 5 pages (revtex4), final version to appear in Phys. Rev.

The self-dual gauge fields and the domain wall fermion zero modes

A new type of gauge fixing of the Coulomb gauge domain wall fermion system that reduces the fluctuation of the effective running coupling and the effective mass of arbitrary momentum direction including the region outside the cylinder cut region is proposed and tested in the $16^3\times 32\times 16$ gauge configurations of RBC/UKQCD collaboration. The running coupling at the lowest momentum point does not show infrared suppression and compatible with the experimental data extracted from the JLab collaboration. The source of the fluctuation of the effective mass near momentum $p=$0.6GeV region is expected to be due to the domain wall fermion zero modes.Comment: 12 pages 2 figures, extended arguments and references adde

Meson masses in large Nf QCD from the Bethe-Salpeter equation

We solve the homogeneous Bethe-Salpeter (HBS) equation for the scalar, pseudoscalar, vector, and axial-vector bound states of quark and anti-quark in large Nf QCD with the improved ladder approximation in the Landau gauge. The quark mass function in the HBS equation is obtained from the Schwinger-Dyson (SD) equation in the same approximation for consistency with the chiral symmetry. Amazingly, due to the fact that the two-loop running coupling of large Nf QCD is explicitly written in terms of an analytic function, large Nf QCD turns out to be the first example in which the SD equation can be solved in the complex plane and hence the HBS equation directly in the time-like region. We find that approaching the chiral phase transition point from the broken phase, the scalar, vector, and axial-vector meson masses vanish to zero with the same scaling behavior, all degenerate with the massless pseudoscalar meson. This may suggest a new type of manifestation of the chiral symmetry restoration in large Nf QCD.Comment: 33 pages, 16 figures. Typos are corrected. Minor corrections and references are added. Version to appear in Phys. Rev.

Asymptotically Free Non-Abelian Gauge Theories With Fermions and Scalars As Alternatives to QCD

In this paper we construct non-Abelian gauge theories with fermions and scalars that nevertheless possess asymptotic freedom.The scalars are taken to be in a chiral multiplet transforming as $(2,2)$ under $SU(2)_L\otimes SU(2)_R$ and transforming as singlets under the colour SU(3) group. We consider two distinct scenarios, one in which the additional scalars are light and another in which they are heavier than half the Z-boson mass. It is shown that asymptotic freedom is obtained without requiring that all additional couplings keep fixed ratios with each other. It is also shown that both scenarios can not be ruled out by what are considered standard tests of QCD like R- parameter, g-2 for muons or deep inelastic phenomena. The light mass scenario is however ruled out by high precision Z-width data (and only by that one data).The heavy mass scenario is still viable and is shown to naturally pass the test of flavour changing neutral currents. It also is not ruled out by precision electroweak oblique parameters. Many distinctive experimental signatures of these models are also discussed.Comment: 37 pages in LATEX with 10 fig

Dynamical gluon mass generation from <A^2> in linear covariant gauges

We construct the multiplicatively renormalizable effective potential for the mass dimension two local composite operator A^2 in linear covariant gauges. We show that the formation of is energetically favoured and that the gluons acquire a dynamical mass due to this gluon condensate. We also discuss the gauge parameter independence of the resultant vacuum energy.Comment: 21 pages. 14 .eps figures. v2: minor modifications. v3: version accepted for publication in JHE

Gluon mass generation in the PT-BFM scheme

In this article we study the general structure and special properties of the Schwinger-Dyson equation for the gluon propagator constructed with the pinch technique, together with the question of how to obtain infrared finite solutions, associated with the generation of an effective gluon mass. Exploiting the known all-order correspondence between the pinch technique and the background field method, we demonstrate that, contrary to the standard formulation, the non-perturbative gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions. We next present a comprehensive review of several subtle issues relevant to the search of infrared finite solutions, paying particular attention to the role of the seagull graph in enforcing transversality, the necessity of introducing massless poles in the three-gluon vertex, and the incorporation of the correct renormalization group properties. In addition, we present a method for regulating the seagull-type contributions based on dimensional regularization; its applicability depends crucially on the asymptotic behavior of the solutions in the deep ultraviolet, and in particular on the anomalous dimension of the dynamically generated gluon mass. A linearized version of the truncated Schwinger-Dyson equation is derived, using a vertex that satisfies the required Ward identity and contains massless poles belonging to different Lorentz structures. The resulting integral equation is then solved numerically, the infrared and ultraviolet properties of the obtained solutions are examined in detail, and the allowed range for the effective gluon mass is determined. Various open questions and possible connections with different approaches in the literature are discussed.Comment: 54 pages, 24 figure

On the Nature of the Phase Transition in SU(N), Sp(2) and E(7) Yang-Mills theory

We study the nature of the confinement phase transition in d=3+1 dimensions in various non-abelian gauge theories with the approach put forward in [1]. We compute an order-parameter potential associated with the Polyakov loop from the knowledge of full 2-point correlation functions. For SU(N) with N=3,...,12 and Sp(2) we find a first-order phase transition in agreement with general expectations. Moreover our study suggests that the phase transition in E(7) Yang-Mills theory also is of first order. We find that it is weaker than for SU(N). We show that this can be understood in terms of the eigenvalue distribution of the order parameter potential close to the phase transition.Comment: 15 page

Catalysis of Dynamical Flavor Symmetry Breaking by a Magnetic Field in 2+12+1 Dimensions

It is shown that in $2+1$ dimensions, a constant magnetic field is a strong catalyst of dynamical flavor symmetry breaking, leading to generating a fermion dynamical mass even at the weakest attractive interaction between fermions. The effect is illustrated in the Nambu-Jona-Lasinio model in a magnetic field. The low-energy effective action in this model is derived and the thermodynamic properties of the model are established. The relevance of this effect for planar condensed matter systems is pointed out.Comment: 11 pages, LaTeX. The final version (with minor corrections) which appeared in Phys.Rev.Lett. 73 (1994) 349

Electroweak symmetry breaking in other terms

We analyse descriptions of electroweak symmetry breaking in terms of ultralocal antisymmetric tensor fields and gauge-singlet geometric variables, respectively; in particular, the Weinberg--Salam model and, ultimately, dynamical electroweak symmetry breaking by technicolour theories with enhanced symmetry groups. Our motivation is to unveil the manifestly gauge invariant structure of the different realisations. We find, for example, parallels to different types of torsion.Comment: 15p