Discrete gauge symmetry anomalies

It has been recently argued that quantum gravity effects strongly violate all non-gauge symmetries. This would suggest that all low energy discrete symmetries should be gauge symmetries, either continuous or discrete. Acceptable continuous gauge symmetries are constrained by the condition they should be anomaly free. We show here that any discrete gauge symmetry should also obey certain “discrete anomaly cancellation” conditions. These conditions strongly constrains the massles fermion content of the theory and follow from the “parent” cancellation of the usual continuous gauge anomalies. They have interesting applications in model building. As an example we consider the constraints on the Z_N “generalized matter parities” of the supersymmetric standard model. We show that only a few (including the standard R-parity) are “discrete anomaly free” unless the fermion content of the minimal supersymmetric standard model is enlarged.     

Patterns of symmetry breaking in supersymmetric gauge theories

We give a group-theoretical analysis of the spontaneous breaking of the gauge group in supersymmetric Yang-Mills theories with unbroken supersymmetry.     

Field dependent nilpotent symmetry for gauge theories

We present predictions for the inclusive production of D mesons at the CERN LHC in the general-mass variable-flavor-number scheme at next-to-leading order. Detailed numerical results are compared to data where available, or presented in a way to ease future comparisons with experimental results. We also point out that measurements at large rapidity have the potential to pin down models of intrinsic charm.     

Translation symmetry breaking in four dimensional lattice gauge theories

We consider lattice gauge theories with finite abelian groupG in the weak coupling regime. It is shown that there is only one translation invariant equilibrium state for the infinite system. In four dimensions we construct a nontranslation invariant equilibrium state, describing an infinite system with localized magnetic flux tube, starting and ending at infinity.     

Renormalization group and dynamical symmetry breakdown in abelian gauge theories

Generalized renormalization group equations are used to analyze the dynamical mechanism of particle mass generation in terms of the Cornwall-Norton model both with and without cut-off. We look for solutions which contain non-zero physical masses of the two fermions (m₁, m₂) and of one of the vector bosons (μ) when the bare masses m_1Λ, m_2Λ, μ_Λ approach zero. For a theory without cut-off we obtain results which are similar to those of Cornwall. For a theory with cut-off the mass generation mechanism may only occur when a bare coupling constant α_Λ of the A_μ vector boson, which remains massless, exceeds some critical value α_c. In this case the fermion masses turn out to be of the superconductivity type.The model's “memory” of the nature of spontaneous symmetry breaking lim_{m1Λ, m2Λ → 0}m_1Λ/m_2Λ ≠ 1 is an indispensible factor for the vector boson to acquire a mass.     

On the character of scalar symmetry breaking in gauge theories

It is shown that the phenomenon of spontaneous breaking of an approximate scale symmetry in gauge theories and the PCAC dynamics are incompatible.     

Renormalization and continuum limit of composite operators in lattice gauge theories

The gluon condensate of dimension 4 is extracted from different operators in a pureSU(2) lattice gauge theory. Multiplicative finite renormalization effects are observed, which are in qualitative agreement with one loop perturbative calculations. Asymptotic scaling is found in the range 2.45≦β≦2.85.     

Infrared saturation and phases of gauge theories with BRST symmetry

We investigate the infrared limit of the quantum equation of motion of the gauge boson propagator in various gauges and models with a BRST symmetry. We find that the saturation of this equation at low momenta distinguishes between the Coulomb, Higgs and confining phase of the gauge theory. The Coulomb phase is characterized by a massless gauge boson. Physical states contribute to the saturation of the transverse equation of motion of the gauge boson at low momenta in the Higgs phase, while the saturation is entirely due to unphysical degrees of freedom in the confining phase. This corollary to the Kugo–Ojima confinement criterion in linear covariant gauges also is sufficient for confinement in general covariant gauges with BRST and anti-BRST symmetry, maximal Abelian gauges with an equivariant BRST symmetry, non-covariant Coulomb gauge and in the Gribov–Zwanziger theory.     

Electron-muon permutation symmetry and multiplicatively conserved lepton number in gauge theories

The similarity between the weak interactions of electron and muon is extended to the principle that all e and μ interactions in gauge models are invariant under e ↔ μ exchange. This necessitates the existence of two Higgs doublets φ_e and φ_μ, and an extended e ↔ μ permutation invariance. After symmetry-breaking, a multiplicatively conserved “permutation parity” π = ± 1 for all particles naturally emerges, with π_μ = −π_e = 1. The model forbids μ → eγ but predicts e⁻e⁻ → μ⁻μ⁻ mediated by π = −1 Higgs bosons at 10⁻¹¹ times the rate of typical weak cross sections.     

Loss of continuum Lorentz invariance in gauge theories on a triangular lattice

On a triangular lattice, a weakly chiral lagrangian of interacting bosons and fermions is constructed to be naturally invariant under the triangular symmetry. The continuum limit of the resulting field theory is not Lorentz invariant. We explicitly show this for the propagator of the massive Schwinger model.     

Massless phases and symmetry restoration in abelian gauge theories and spin systems

We give a new, elementary proof for the existence of a deconfining transition to a massless (QED) phase in the four-dimensionalU(1) lattice gauge theory and of an intermediate QED phase, accompanied by dynamical restoration of localU(1) invariance, in the four dimensional _N models, withN large. Our methods can also be used to prove the existence of a phase transition in theXY model in three or more dimensions, in three- and four-dimensional abelian Higgs models, and in more general models admitting some local, abelian gauge invariance.Work supported in part by the NSF under grant DMR 81-00417     

Generalized local gauge symmetry and the Ward-Takahashi identities in unified field theories

We discuss the symmetry basis of unified field theories, i.e., the generalized concept of local gauge symmetry, and its physical implications. The generalized Ward-Takahashi identities and the explicit constraints among renormalization constants are derived by using the path integral in a specific model. These constraints are confirmed at the one-loop level.Work supported in part by the U.S. Energy Research and Development Administration.     

The many-body content of quantum gauge theories and spontaneous symmetry breaking

The many-body content of quantum field theories is studied by performing the limit velocity of light → ∞. It is found that the limit of the Goldstone model is the Bogoliubov model of superfluidity, and the limit of the vacuum of spontaneously broken abelian theories is a plasma whose excitations are the limit of the massive gauge bosons. The method appears suitable to study dynamical supersymmetry breaking and colour confinement.     

A well-defined transition from continuum to lattice formulation of gauge field theories

In this paper it is shown that the well-known expressions for the action of lattice gauge theories (abelian and nonabelian) can be derived in a well-defined manner from corresponding nonlocal expressions once we take the local limit. First, a nonlocal formulation of the spinorial part of the QED action, accomplished 30 years ago, is extended to the Maxwell field part. Subsequently, the nonlocal action is discretized in the conventional way yielding, in the local limit, the well-known form of the lattice action. The above procedure is successfully repeated for nonabelian gauge fields.