Topological gauge theories and group cohomology

We show that three dimensional Chern-Simons gauge theories with a compact gauge groupG (not necessarily connected or simply connected) can be classified by the integer cohomology groupH ⁴(BG,Z). In a similar way, possible Wess-Zumino interactions of such a groupG are classified byH ³(G,Z). The relation between three dimensional Chern-Simons gauge theory and two dimensional sigma models involves a certain natural map fromH ⁴(BG,Z) toH ³(G,Z). We generalize this correspondence to topological spin theories, which are defined on three manifolds with spin structure, and are related to what might be calledZ ₂ graded chiral algebras (or chiral superalgebras) in two dimensions. Finally we discuss in some detail the formulation of these topological gauge theories for the special case of a finite group, establishing links with two dimensional (holomorphic) orbifold models.     

Convergence of Migdal-Kadanoff iterations in non-abelian lattice gauge models

We study the Migdal-Kadanoff recursion relations for lattice gauge models with gauge groups SU(N) or U(N) in dimensionsd<4. It is shown that the Gibbs factor of a plaquette with Wilson action is driven to 1 for all values of the temperature (coupling constant). For models recently proposed by K. R. Ito, where Migdal's and Kadanoff's recursion relations hold exactly, a lower bound on the string tension is derived. The results obtained by us extend those derived by Ito for U(1). Our method is based on analytic continuation of the Gibbs factors, which are class functions, in the central angles.     

Body fixed frame,rigid gauge rotations and largeN random fields in QCD

The body fixed frame with respect to local gauge transformations is introduced. Rigid gauge rotations in QCD and their Schrödinger equation are studied for static and dynamic quarks. Possible choices of the rigid gauge field configuration corresponding to a nonvanishing static colormagnetic field in the body fixed frame are discussed. A gauge invariant variational equation is derived in this frame. For large numberN of colors the rigid gauge field configuration is regarded as random with maximally random probability distribution under constraints on macroiscopic-like quantities. For the uniform magnetic field the joint probability distribution of the field components is determined by maximizing the appropriate entropy under the area law constraint for the Wilson loop. In the quark sector the gauge invariance requires the rigid gauge field configuration to appear not only as a background but also as inducing an instantaneous quark-quark interaction. Both are random in the largeN limit.Communicated by F. Lenz     

Gauge theory in deformed $$ \mathcal{N} $$ = (1, 1) superspace

We review the non-anticommutative Q-deformations of = (1, 1) supersymmetric theories in four-dimensional Euclidean harmonic superspace. These deformations preserve chirality and harmonic Grassmann analyticity. The associated field theories arise as a low-energy limit of string theory in specific backgrounds and generalize the Moyal-deformed supersymmetric field theories. A characteristic feature of the Q-deformed theories is the half-breaking of supersymmetry in the chiral sector of the Euclidean superspace. Our main focus is on the chiral singlet Q-deformation, which is distinguished by preserving the SO(4) ∼ Spin(4) “Lorentz” symmetry and the SU(2) R-symmetry. We present the superfield and component structures of the deformed = (1, 0) supersymmetric gauge theory as well as of hypermultiplets coupled to a gauge superfield: invariant actions, deformed transformation rules, and so on. We discuss quantum aspects of these models and prove their renormalizability in the Abelian case. For the charged hypermultiplet in an Abelian gauge superfield background we construct the deformed holomorphic effective action. The text was submitted by the authors in English.     

Gauge-Invariant Chiral Schwinger Model with Faddeevian Regularization: Stueckelberg Term, Operator Solution, and Hamiltonian and BRST Formulations

A chiral Schwinger model with the Faddeevian regularization à la Mitra is studied in one-space one-time dimension in the conventional form of dynamics (on the hyperplanes x ⁰ = constant) called the Instant-Form (IF) dynamics. The original IF theory is seen to be gauge-noninvariant (GNI). Corresponding to this GNI model, a gauge-invariant (GI) theory is constructed through the so-called Stueckelberg term. The operator solution and the Hamiltonian and BRST formulations of the resulting GI theory, obtained by the inclusion of the Stueckelberg term in the action of the original GNI theory, are then investigated with some specific gauge choices. The physical contents of the original GNI theory are also recovered from the newly constructed GI theory under a special gauge.     

O(5)×U(1) electroweak gauge theory and the neutrino oscillations in matter

A study is made of the groupO(5)×U(1). The group is economical in the number of gauge bosons, which we associate with each of its generators, and is anomaly-free. The left-handed leptonsL _L ^T (v _e ,e,,v ) _L are assigned to the four-dimensional spinorial representations ofO(5). The right-handed particles are taken to be the singlets of the group. The theory has three sets of gauge bosons: (1) analogues of the GWS model, (2) additional charged gauge bosons, and (3) a set of three additional neutral gauge bosons as compared to the GWS model. We introduce neutrino mixing by mixing the additional charged gauge bosons. We develope a theory of neutrino oscillations in matter in such a way that in the absence of matter the scattering length reduces to the usual scattering length in vacuum. Even if the neutrino masses are equal or the neutrinos are massless, we still have neutrino oscillations in matter, a result already noted by Wolfenstein.     

Proof of chiral symmetry breaking in lattice gauge theory

Using the method of infrared bounds and partial-integration formulas, we prove that there is a chiral phase transition in four-dimensional strongly coupled lattice gauge theory with gauge group U(N) and staggered fermions for all N5.     

Minimal left-right symmetric models and new <Emphasis Type="Italic">Z</Emphasis>’ properties at future electron-positron colliders

It was recently shown that left-right symmetric models for elementary particles can be built with only two Higgs doublets. The general consequence of these models is that the left and right fermionic sectors can be connected by a new neutral gauge boson Z having its mass as the only additional new parameter. In this paper we study the influence of the fundamental fermionic representation for this new neutral gauge boson. Signals of possible new heavy neutral gauge bosons are investigated for the future electron-positron colliders at GeV, 1 TeV and 3 TeV. The total cross sections, forward-backward and left-right asymmetries and model differences are calculated for the process . Bounds on Z masses are estimated.Received: 4 May 2004, Revised: 22 September 2004, Published online: 9 November 2004     

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     

Melting Crystal, Quantum Torus and Toda Hierarchy

Searching for the integrable structures of supersymmetric gauge theories and topological strings, we study melting crystal, which is known as random plane partition, from the viewpoint of integrable systems. We show that a series of partition functions of melting crystals gives rise to a tau function of the one-dimensional Toda hierarchy, where the models are defined by adding suitable potentials, endowed with a series of coupling constants, to the standard statistical weight. These potentials can be converted to a commutative sub-algebra of quantum torus Lie algebra. This perspective reveals a remarkable connection between random plane partition and quantum torus Lie algebra, and substantially enables to prove the statement. Based on the result, we briefly argue the integrable structures of five-dimensional supersymmetric gauge theories and A-model topological strings. The aforementioned potentials correspond to gauge theory observables analogous to the Wilson loops, and thereby the partition functions are translated in the gauge theory to generating functions of their correlators. In topological strings, we particularly comment on a possibility of topology change caused by condensation of these observables, giving a simple example.     

Non-perturbative renormalization group functions in (2+1)-dimensional supersymmetric gauge theories

Three-dimensional supersymmetric Higgs models with an additional U(N) flavor symmetry are considered within the 1/N expansion. Explicit expressions for the renormalization group functions are obtained in the large N limit which exhibit logarithmic dependence on the gauge coupling constants.     

Anisotropic cosmological models of Bianchi types III and V in Lyra's geometry

Exact solutions to Einstein's equations are presented in vacuum and in the presence of stiff matter for spatially homogeneous cosmological models of Bianchi types type III and V in the normal gauge for Lyra's geometry. Solutions represent anisotropic cosmological universes which contract from infinite volume at the initial time singularityT=0 to zero volume asT. Some physical properties of the models are also discussed.     

Charged tensor matter fields and Lorentz symmetry violation via spontaneous symmetry breaking

We consider a model with a charged vector field along with a Cremmer-Scherk-Kalb-Ramond (CSKR) matter field coupled to a U(1) gauge potential. We obtain a natural Lorentz symmetry violation due to the local U(1) spontaneous symmetry breaking mechanism triggered by the imaginary part of the vector matter. The choice of the unitary gauge leads to the decoupling of the gauge-KR sector from the Higgs-KR sector. The excitation spectrum is carefully analyzed and the physical modes are identified. We propose an identification of the neutral massive spin-1 Higgs-like field with the massive Z boson of the so-called mirror matter models.Received: 30 October 2003, Revised: 16 March 2004, Published online: 23 June 2004     

High scale perturbative gauge coupling in R-parity conserving SUSY <Emphasis Type="Italic">SO</Emphasis>(10) with longer proton lifetime

It is well known that in single step breaking of R-parity conserving SUSY SO(10) that needs the Higgs representations , the GUT gauge coupling violates the perturbative constraint at mass scales a few times larger than the GUT scale. Therefore, if the SO(10) gauge coupling is to remain perturbative up to the Planck scale ( GeV), the scale M_U of the GUT symmetry breaking is to be bounded from below. The bound depends upon specific Higgs representations used for SO(10) symmetry breaking but, as we find, cannot be lower than $1.5 \times 10$¹⁷ GeV. In order to obtain such a high unification scale we propose a two-step SO(10) breaking through SU(2)_L $\times$ SU(2)_R $\times$ U(1)_B-L $\times$SU(3)_C ( ) intermediate gauge symmetry. We estimate the potential threshold and gravitational corrections to the gauge coupling running and show that they can make the picture of perturbative gauge coupling running consistent at least up to the Planck scale. We also show that when by the Higgs representations , gravitational corrections alone with negligible threshold effects may guarantee such perturbative gauge coupling. The lifetime of the proton is found to increase by nearly 6 orders over the present experimental limit for . For the proton decay mediated by a dim = 5 operator a wide range of lifetimes is possible, extending from the current experimental limit up to values 2-3 orders longer. Received: 1 July 2005, Revised: 21 August 2005, Published online: 11 October 2005     

p-Form electrodynamics

A generalization of gauge theory in which the gauge potential1-form is replaced by a p-form is studied. Charged particles are then replaced by elementary extended objects of dimension p–1. It is shown that this extension is compatible with space-time locality only if the gauge group is U(1). A source which is a closed p–1 surface has zero total charge and corresponds to a particle-antiparticle pair. Its quantum rate of production in an external uniform field is evaluated semiclassically. The analog of the Dirac magnetic pole is constructed. It is another extended object, of dimension n–p–3, where n is the dimension of space-time. The electric and magnetic charges obey the Dirac quantization condition. This condition is derived in two different ways. One method makes use of local gauge patches and the other brings in singular gauge transformations. A topological mass term is introduced and it is shown that it can coexist with a magnetic pole when n=2p+1, provided the topological mass is quantized.     

Canonical local algorithms for spin systems: heat bath and Hasting’s methods

We introduce new fast canonical local algorithms for discrete and continuous spin systems. We show that for a broad selection of spin systems they compare favorably to the known ones except for the Ising 1 spins. The new procedures use discretization scheme and the necessary information have to be stored in computer memory before the simulation. The models for testing discrete spins are the Ising 1, the general Ising S or Blume-Capel model, the Potts and the clock models. The continuous spins we examine are the O(N) models, including the continuous Ising model (N = 1), the Ising model (N = 1), the XY model (N = 2), the Heisenberg model (N = 3), the Heisenberg model (N = 3), the O(4) model with applications to the SU(2) lattice gauge theory, and the general O(N) vector spins with .Received: 16 August 2004, Published online: 21 October 2004PACS: 05.70.Fh Phase transitions: general studies - 64.60.Cn Order-disorder transformations; statistical mechanics of model systems - 75.10.Hk Classical spin models - 75.10.Nr Spin-glass and other random models     

Elliptic operators in the functional quantisation for gauge field theories

Given a gauge theory with gauge groupG acting on a path spaceX,G andX being both infinite dimensional manifolds modelled on spaces of sections of vector bundles on a compact riemannian manifold without boundary, it is shown that when the action ofG onX is smooth, free and proper, the same ellipticity condition on an operator naturally given by the geometry of the problem yields both the existence of a principal fibre bundle structure induced by the canonical projection :XX/G and the existence of the Faddeev-Popov determinant arising in the functional quantisation of the gauge theory. This holds for certain gauge theories with anomalies like bosonic closed string theory in non-critical dimension and also holds for a class of gauge theories which includes Yang-Mills theory.     

Every gauge orbit passes inside the Gribov horizon

TheL ² topology is introduced on the space of gauge connectionsA and a natural topology is introduced on the group of local gauge transformationsGT. It is shown that the mappingGT×AA defined byAA ^g=g^*Ag+g^*dg is continuous and that each gauge orbit is closed. The Hilbert norm of the gauge connection achieves its absolute minimum on each gauge orbit, at which point the orbit intersects the region bounded by the Gribov horizon.CNR, GNFMResearch supported in part by the National Science Foundation under grant no. PHY 87-15995     

Gauge fluctuations in superconducting films

In this paper we consider a type-I superconducting film modeled by the Ginzburg-Landau model, confined between two parallel planes a distance L apart from one another. Our approach is based on the Gaussian effective potential in the transverse unitarity gauge, which allows to treat gauge contributions in a compact form. Using techniques from dimensional and -function regularizations, modified by the confinement conditions, we investigate the critical temperature as a function of the film thickness L. The contributions from the scalar self-interaction and from the gauge fluctuations are clearly identified. The model suggests the existence of a minimal critical thickness below which superconductivity is suppressed. A comparison with present experimental observations is done.Received: 19 December 2003, Published online: 9 April 2004PACS: 74.20.-z Theories and models of superconducting state - 11.15.Ex Spontaneous breaking of gauge symmetries - 05.10.Cc Renormalization group methods     

Light-Front Hamiltonian and BRST Formulations of a Two-Dimensional Abelian Higgs Model in the Broken Symmetry Phase

The light-front Hamiltonian and BRST formulations of an abelian Higgs model involving the electromagnetic vector gauge field are investigated in one space, one time dimension in the broken symmetry phase, where the phase (x, t) of the complex matter field (x, t) carries the charge degree of freedom of the complex matter field and is, in fact, akin to the Goldstone boson.