Symmetry breaking and time variation of gauge couplings

Astrophysical indications that the fine structure constant has undergone a small time variation during the cosmological evolution are discussed within the framework of the standard model of the electroweak and strong interactions and of grand unification. A variation of the electromagnetic coupling constant could either be generated by a corresponding time variation of the unified coupling constant or by a time variation of the unification scale, of by both. The various possibilities, differing substantially in their implications for the variation of low energy physics parameters like the nuclear mass scale, are discussed. The case in which the variation is caused by a time variation of the unification scale is of special interest. It is supported in addition by recent hints towards a time change of the proton–electron mass ratio. Implications for the analysis of the Oklo remains and for quantum optics tests are discussed.     

Symmetry breaking and asymptotic freedom in colour SU(3) gauge models

A class of quark models based on the colour gauge group SU(3) is shown to be asymptotically free despite the conplete breakdown of local symmetry to guarantee infrared stability. The symmetry breakdown is achieved by the presence of elementary scalar fields either through the Higgs mechanism or dynamically as first proposed by Coleman and Weinberg. Asymptotic freedom is preserved by imposing eigenvalue conditions on the coupling constants as first proposed by Chang. New quark species must be present, but below their production threshold, colour can still be a global symmetry which is approximate under SU(3), but exact under SU(2). Among the many implications of this class of models is the possibility of producing isolated quarks and gluons of non-zero mass without altering the short-distance behaviour of the superstrong interaction which binds them.     

Symmetry breaking and restoration for interacting scalar and gauge fields in Lifshitz type theories

We consider the one-loop effective potential at zero and finite temperature in field theories with anisotropic space–time scaling, with critical exponent z=2$z=2$, including both scalar and gauge fields. Depending on the relative strength of the coupling constants for the gauge and scalar interactions, we find that there is a symmetry breaking term induced at one loop at zero temperature and we find symmetry restoration through a first-order phase transition at high temperature.     

Symmetry breaking by instantons in supergravity

The non-zero modes of different spin operators on the background of a self-dual gravitational instanton are all related by global supersymmetry transformations and completely cancel in the one-loop term, which is determined entirely by the zero modes. We derive the number of zero modes of each spin. In an asymptotically locally Euclidean self-dual instanton there are 2τ $\text{spin}\text{-}\text{3}\text{2}$ zero modes and 3τ spin-2 zero modes, where τ is the Hirzebruch signature. Up to 3 of the spin-2 zero modes (depending on boundary conditions) may correspond to global rotations. The $\text{spin}\text{-}\text{3}\text{2}$ zero modes break the U(1) chiral symmetry and give rise to helicity-changing amplitudes. Together with the spin-2 zero modes they determine the trace anomaly or scaling behaviour. We can compare our results with the perturbation theory predictions for the axial vector current and trace anomalies in K3, the unique compact self-dual gravitational instanton, because in this case there are no boundary terms. We obtain agreement.     

The quark-gluon vertex in Landau gauge QCD: Its role in dynamical chiral symmetry breaking and quark confinement

The infrared behavior of the quark-gluon vertex of quenched Landau gauge QCD is studied by analyzing its Dyson-Schwinger equation. Building on previously obtained results for Green functions in the Yang-Mills sector, we analytically derive the existence of power-law infrared singularities for this vertex. We establish that dynamical chiral symmetry breaking leads to the self-consistent generation of components of the quark-gluon vertex forbidden when chiral symmetry is forced to stay in the Wigner-Weyl mode. In the latter case the running strong coupling assumes an infrared fixed point. If chiral symmetry is broken, either dynamically or explicitly, the running coupling is infrared divergent. Based on a truncation for the quark-gluon vertex Dyson-Schwinger equation which respects the analytically determined infrared behavior, numerical results for the coupled system of the quark propagator and vertex Dyson-Schwinger equation are presented. The resulting quark mass function as well as the vertex function show only a very weak dependence on the current quark mass in the deep infrared. From this we infer by an analysis of the quark-quark scattering kernel a linearly rising quark potential with an almost mass independent string tension in the case of broken chiral symmetry. Enforcing chiral symmetry does lead to a Coulomb type potential. Therefore, we conclude that chiral symmetry breaking and confinement are closely related. Furthermore, we discuss aspects of confinement as the absence of long-range van der Waals forces and Casimir scaling. An examination of experimental data for quarkonia provides further evidence for the viability of the presented mechanism for quark confinement in the Landau gauge.     

Symmetry breaking induced by a magnetic field in a quasi-two-dimensional d-wave superconductor

A model of quasi-two-dimensional d-wave superconductor, with strong nesting properties of the Fermi surface is considered. The orbital effect of a moderate magnetic field applied perpendicularly to the conducting planes is studied in the mean field approximation. It is shown that the field can induce a time reversal symmetry breaking SDW order coexisting with the superconducting order and can open a gap over the whole Fermi surface. The anomalies recently observed in the heat conductivity in might be ascribed to this effect. Received 7 May 1999 and Received in final form 13 August 1999     

Symmetry breaking and duality diagrams in a multiparticle production model

Symmetry breaking is studied systematically in a multi-Regge resonance production model. Consistency of the planar bootstrap with broken symmetry requires ideal nonets to have equal spacing between ?, K¹ and φ trajectories. Non-planar diagrams generate a leading vacuum singularity near one. Formulae relating symmetry breaking of the pomeron couplings and of produced particle multiplicities are given.     

Symmetry and symmetry breaking in generalized parastatistics

An analysis is made of the characteristics of internal symmetry and symmetry breaking in a quantum field theory with generalized parastatistics, defined by either double commutation relations or single commutation relations. The connection between the two statistics is clarified. We develop a formalism in which statistics is viewed as a dynamical or phase variable of quantum systems. It is shown that the types of Higgs phases possible depend upon statistics. Relationships between physical amplitudes implied by internal symmetry with normal statistics are violated in the case of generalized parastatistics.     

Reply to Lemke's comment on a paper by Gonzalez-Gascon

The distortions introduced in a recent paper (for v > 1) are unavoidable and the “experimentally measured distortions” quoted by Lemke are not distortions at all.     

Symmetry breaking in a supersymmetric model of strong and electroweak interactions

We describe a supersymmetric model of strong and electroweak interactions based on the gauge groupSU(3)×SU(2)×U(1)×?(1). We concentrate on the pattern of the spontaneous symmetry breaking by the tree level scalar potential. It is possible to break the?(1) factor at superlarge energies relative to the simultaneous breaking scale ofSU(2)×U(1) and supersymmetry. The model has?(1) anomalies. Attempts to make an anomaly-free model based on the groupE ₆ are described. We also comment on possible modifications of the?(1) anomaly problem due to gravitational effects.     

Supersymmetry breaking and gauge mediation in models with a generic superpotential

We present a general scheme for finding or creating a metastable vacuum in supersymmetric theories. By using the formalism, we show that there is a parameter region where a metastable vacuum exists in the Wess–Zumino model coupled to messenger fields. This model serves as a perturbative renormalizable model of direct gauge mediation.     

Symmetry breaking and enhanced condensate fraction in a matter-wave bright soliton

An exact diagonalization study reveals that a matter-wave bright soliton and the Goldstone mode are simultaneously created in a quasi-one-dimensional attractive Bose-Einstein condensate by superpositions of quasidegenerate low-lying many-body states. Upon formation of the soliton the maximum eigenvalue of the single-particle density matrix increases dramatically, indicating that a fragmented condensate converts into a single condensate as a consequence of the breaking of translation symmetry.     

Infrared exponents and the strong-coupling limit in lattice Landau gauge

We study the gluon and ghost propagators of lattice Landau gauge in the strong-coupling limit β=0 in pure SU(2) lattice gauge theory to find evidence of the conformal infrared behavior of these propagators as predicted by a variety of functional continuum methods for asymptotically small momenta $q^{2}\ll\varLambda_{\mathrm{QCD}}^{2}$ . In the strong-coupling limit, this same behavior is obtained for the larger values of a ² q ² (in units of the lattice spacing a), where it is otherwise swamped by the gauge-field dynamics. Deviations for a ² q ²<1 are well parameterized by a transverse gluon mass ∝1/a. Perhaps unexpectedly, these deviations are thus no finite-volume effect but persist in the infinite-volume limit. They furthermore depend on the definition of gauge fields on the lattice, while the asymptotic conformal behavior does not. We also comment on a misinterpretation of our results by Cucchieri and Mendes (Phys. Rev. D 81:016005, 2010).     

Fermions in random gauge fields and chiral-symmetry breaking

Random superpositions of gauge fields such that a fermion can propagate in them along the same one-dimensional trajectory in four-dimensional space over arbitrary distances without reduction of the amplitude are considered. Conditions are found under which such structures possess a finite density of fermion zero modes. The possibility of chiral-symmetry breaking in these configurations of gauge fields is explored.     

Symmetry breaking and restoration in Lifshitz type theories

We consider the one-loop effective potential at zero and finite temperature in scalar field theories with anisotropic space-time scaling. For z=2, there is a symmetry breaking term induced at one loop at zero temperature and we find symmetry restoration through a first-order phase transition at high temperature. For z=3, we considered at first the case with a positive mass term at tree level and found no symmetry breaking effects induced at one loop, and then we study the case with a negative mass term at tree level where we cannot conclude about symmetry restoration effects at high temperature because of the imaginary parts that appear in the effective potential for small values of the scalar field.