Homology and abelian lattice gauge theories

A simple Abelian model with both Higgs and gauge field degrees of freedom is investigated on a simplicial lattice of arbitrary dimension. We use group character expansion for both fields to get a diagrammatic expansion of the partition function. The diagrams consist of gauge group representation valued 1- and 2-chains. The diagrams are proved to satisfy the constraint that the boundary of the 2-chain representing the gauge field is equal to the 1-chain representing the Higgs field. Otherwise they identically vanish. Simple consequences of this are current conservation and the vanishing of non-null-homologous Wilson loops. Finally we use this picture for giving a lowest order estimate for the critical length of a string. This is the length at which the flux-tube string connecting two opposite charges is likely to break into two pieces due to pair creation.     

Composite Higgs scalars

We construct models in which the Higgs doublet whose vacuum expectation breaks SU(2) × U(10 is a bound state of massive strongly interacting fermions. The couplings of the composite Higgs to ordinary fermions are induced by heavy gauge boson exchange in the manner of extended technicolor. Other heavy gauge bosons generate a negative mass term for the Higgs.     

NONLOCAL CURRENTS AS NOETHER CURRENTS DUE TO A NONLOCALLY TRANSFORMED GLOBAL SYMMETRY

In this paper we first present the gauge invariant conserved Noether current for the Yang-Mi11s theory, which is nonlocal is some sense. Then we introduce for the two dimensional chiral model, plain and supersymmetric, the nonlocal one-complex parameter-dependent symmetric generators, which shift the Lagrangian density by a total divergence. Both the equations of motion and the energy momentum density are tnvaunt. The associated ically Into infinite Noether current may be expanded analyt-series of nonlocal currents.     

A disorder parameter that test for confinement in gauge theories with quark fields

We propose to use a suitably defined vortex free energy as a disorder parameter in gauge field theories with matter fields. It is supposed to distinguish between the confinement phase, massless phase(s) and Higgs phase where they exist. The matter fields may transform according to an arbitrary representation of the gauge group. We compute the vortex free energy by series expansion for a Z₂ Higgs model and for SU(2) lattice models with quark or Higgs fields in the fundamental representation at strong coupling (confinement phase), and for the Z₂ Higgs model in the range of validity of low-temperature expansions (Higgs phase). The results are in agreement with the expected behavior.     

Perturbative gauge invariance: electroweak theory II

A recent construction of the electroweak theory, based on perturbative quantum gauge invariance alone, is extended to the case of more generations of fermions with arbitrary mixing. The conditions implied by second order gauge invariance lead to an isolated solution for the fermionic couplings in agreement with the standard model. Third order gauge invariance determines the Higgs potential. The resulting massive gauge theory is manifestly gauge invariant, after construction.     

Static finite-energy solutions of gauge fields with separated radial variable

For arbitrary compact gauge group G and real representations of the Higgs fields, we seek static finite-energy solutions for which the radial dependence of the fields is factorized. We find that the gauge fields vanish outside a fixed SO(3) subgroup of G, and that inside SO(3) they reduce to the 't Hooft-Polyakov solution with unit magnetic charge. The Higgs fields may belong to any integer representation of this SO(3).     

Electroweak chiral Lagrangian for left–right symmetric models: The matter sector

The matter sector of electroweak chiral Lagrangian up to dimension four operators for left–right symmetric models with a neutral light Higgs is provided. The connection of these operators to Yukawa couplings, anomalous gauge couplings and parameters in the matter sector of conventional electroweak chiral Lagrangian is made. It is shown that there exists proper parameter space to loosen constraint for the mass of right handed gauge boson from the mass difference of neutral K meson.     

The vortex free energy in the screening phase of the Z(2) Higgs model

The vortex free energy was proposed to distinguish between the confinement and the Higgs phase (in the sense of 't Hooft) in lattice gauge theory, when matter fields are present that transform according to an arbitrary representation of the gauge group. In this paper I consider the Z(2) Higgs model and calculate the vortex free energy in the screening part of the confining/screening phase of Fradkin and Shenker. The result does not agree with the expected behavior that corresponds to the structure of the phase diagram. Therefore the vortex free energy is no longer a good indicator for confinement when matter fields transform non-trivially under the center of the gauge group (such as Z(2) Higgs scalars).     

A FURTHER DISCSSION on THE GAUGE HIERARCHY

In this paper we have calulated the Higgs potential with the one-loop correction in the SU(3) and SU(5) gauge models. The result shows that the arbitrary gauge hierarchy is doubtful in the peiturbation theory. This is in contrdiction with the conclusion obtained by Mohaptra et al.     

Gauge invariant formulation of non-Abelian chiral gauge theories in two dimensions

We study the gauge invariant version of a chiral non-Abelian gauge theory. A local bosonic effective action is obtained and the covariant conservation of the gauge current is verified. A Hamiltonian analysis of the model and of its constraints is performed. We show that the constraints are first class and that no anomalous term appears in the commutators of the gauge group generators. The current algebra of the model is obtained and the gauge fixing is analyzed.     

Chern-Simons Gauge Theory and Ginzburg-Landau Type Theories: (Ⅰ) Abelian Cases

We show that after the spontaneous symmetry breaking has taken place the Abelian Higgs models with or without the Chern-Simons term would satisfy the same field equation with the massive Chern-Simons gauge theory and have the same anyon solutions. So we regard the massive Chern-Simons gauge theory as an effective gauge theory of the Abelian Higgs models.     

Noncontractible hyperloops in gauge models with Higgs fields in the fundamental representation

We study finite-energy configurations in SO(N) gauge theories with Higgs fields in the fundamental representation. For all winding numbers, noncontractible hyperloops are constructed. The corresponding energy density is spherically symmetric, and the configuration with maximal energy on each hyperloop can be determined. Noncontractible hyperloops with an arbitrary winding number for SU(2) gauge theory are also given.     

Space-time symmetries in gauge theories

A general definition of symmetries of gauge fields is proposed and a method developed for constructing symmetric fields for an arbitrary gauge group. Scalar fields occur naturally in the formalism and the pure gauge theory reduces to a Higgs model in lower dimensions.Laboratoire propre du C.N.R.S. associé à l'Ecole Normale Supérieure et à l'Université de Paris Sud     

Classical gauge theories as dynamical systems—Regularity and chaos

In this review we present the salient features of dynamical chaos in classical gauge theories with spatially homogeneous fields. The chaotic behaviour displayed by both abelian and non-abelian gauge theories and the effect of the Higgs term in both cases are discussed. The role of the Chern-Simons term in these theories is examined in detail. Whereas, in the abelian case, the pure Chern-Simons-Higgs system is integrable, addition of the Maxwell term renders the system chaotic. In contrast, the non-abelian Chern-Simons-Higgs system is chaotic both in the presence and the absence of the Yang-Mills term. We support our conclusions with numerical studies on plots of phase trajectories and Lyapunov exponents. Analytical tests of integrability such as the Painlevé criterion are carried out for these theories. The role of the various terms in the Hamiltonians for the abelian Higgs, Yang-Mills-Higgs and Yang-Mills-Chern-Simons-Higgs systems with spatially homogeneous fields, in determining the nature of order-disorder transitions is highlighted, and the effects are shown to be counter-intuitive in the last-named system.     

Can the nearly conformal sextet gauge model hide the Higgs impostor?

New results are reported from large scale lattice simulations of a frequently discussed strongly interacting gauge theory with a fermion flavor doublet in the two-index symmetric (sextet) representation of the SU(3) color gauge group. We find that the chiral condensate and the mass spectrum of the sextet model are consistent with chiral symmetry breaking in the limit of vanishing fermion mass. In contrast, sextet fermion mass deformations of spectral properties are not consistent with leading conformal scaling behavior near the critical surface of a conformal theory. A recent paper could not resolve the conformal fixed point of the gauge coupling from the slowly walking scenario of a very small nearly vanishing β-function (DeGrand et al. [3]). It is argued that overall consistency with our new results is resolved if the sextet model is close to the conformal window, staying outside with a very small non-vanishing β-function. The model would exhibit then the simplest composite Higgs mechanism leaving open the possibility of a light scalar state with quantum numbers of the Higgs impostor. It would emerge as the pseudo-Goldstone dilaton state from spontaneous symmetry breaking of scale invariance. We will argue that even without association with the dilaton, the scalar Higgs-like state can be light very close to the conformal window. A new Higgs project of sextet lattice simulations is outlined to resolve these important questions.     

Phase factors,point-splitting regularisation and chiral anomalies

A method is proposed to construct the path-independent form of phase factors pertaining to non-abelian gauge theories. It is found that the original form of the phase factor, as envisaged by Schwinger, is reproduced for a straight path. As an illustration of its use this work is applied, within the framework of point-splitting regularisation, to obtain the familiar axial anomaly in a pure vector gauge theory. Subtleties associated with the treatment of the vector gauge current are also discussed. Finally, the scheme of computations is employed to derive the covariant and consistent anomalies in a non-abelian chiral gauge theory in arbitrary even dimensions.     

Solution to constraints in Wess-Zumino supergravity formalism

We explicitly solve the constraints of the superfield supergravity formalism of Wess and Zumino, for an arbitrary gauge, in terms of superfields. Wess and Zumino's action turns out to be identical to one of a class of actions found earlier by the author: the one with the minimal set of auxiliary fields. We also show how to write chiral Lagrangians, including the cosmological term and the Lagrangian for conformal supergravity.     

Exact consequences of universality in SU(2) × U(1) gauge models

Exact consequences of universality within SU(2) × U(1) gauge models, with leptons in doublets and singlets, and for arbitrary vacuum expectation values of the Higgs fields, imply an extended Weinberg-Salam structure for leptons, with all neutrinos massless (the inverse statement is obvious). We also discuss approximate universality.     

Flavour dynamics with general scalar fields

We consider a spontaneously broken gauge theory based on the standard model (SM) group with scalar fields that carry arbitrary representations of G, and we investigate some general properties of the charged and neutral current involving these fields. In particular we derive the conditions for having real or complex couplings of the Z boson to two different neutral or charged scalar fields, and for the existence of CP-violating Z-scalar-scalar couplings. Moreover, we study models with the same fermion content as in the SM, with one SU(2) Higgs singlet, and an arbitrary number of Higgs doublets. We show that the structure of the Z-Higgs boson and of the Yukawa couplings in these models can be such that CP-violating form factors which conserve chirality are induced at the one-loop level. Received: 18 December 1998 / Published online: 22 March 1999     

Dynamics of N = 2 supersymmetric gauge theories in three dimensions

We study the structure of the moduli spaces of vacua and superpotentials of N = 2 supersymmetric gauge theories in three dimensions. By analyzing the instanton corrections, we compute the exact superpotentials and determine the quantum Coulomb and Higgs branches of the theories in the weak coupling regions. We find candidates for non-trivial N = 2 superconformal field theories at the singularities of the moduli spaces. The analysis is carried out explicitly for gauge groups U(N_c) and SU(N_c) with N _f flavors. We show that the field theory results are in complete agreement with the intersecting branes picture. We also compute the exact superpotentials for arbitrary gauge groups and arbitrary matter content.