Dimensional regularization of gauge theories in spherical spacetime: Free field trace anomalies

The O(n + 1) covariant formulation of massless quantum electrodynamics in spherical spacetime is further developed to allow a calculation of the energy-momentum tensor trace anomalies for the free Dirac, electromagnetic, and SU(2) gauge fields. The principal technical development is the construction of the Faddeev-Popov ghosts for electrodynamics and SU(2) Yang-Mills theory. This construction is unconventional first in that the gauge fixing term in the Lagrangian is not a perfect square, and second because it is necessary to remove radial as well as gauge degrees of freedom from the measure of the functional integral. The ghost fields are shown to satisfy a minimal scalar field equation. The free field effective action is found to be divergent in four dimensions, and is renormalized by the inclusion in the Lagrangian of a counterterm local in the gravitational fields. The energy-momentum tensor calculated from this renormalized effective action is shown to have a trace anomaly.     

Towards a finite N = 2 susy GUT

We consider finite, N = 2 supersymmetric GUTs based on gauge groups SU(n) and SO(n). As an example, we discuss a semirealistic model based on SO(12). We argue that in finite, N = 2 supersymmetric GUTs, gauge symmetry breaking should occur dynamically. We present a heuristic picture in which this is induced by soft, finiteness preserving SUSY breaking terms. The bound states formed cause a very rapid evolution of the SO(12) coupling constant and break SO(12) into SU(4)×SU(3)_C×U(1).     

Topological Geon Black Holes in Einstein-Yang-Mills Theory

We construct topological geon quotients of two families of Einstein-Yang-Mills black holes. For Künzle??s static, spherically symmetric SU(n) black holes with n?>?2, a geon quotient exists but generically requires promoting charge conjugation into a gauge symmetry. For Kleihaus and Kunz??s static, axially symmetric SU(2) black holes a geon quotient exists without gauging charge conjugation, and the parity of the gauge field winding number determines whether the geon gauge bundle is trivial. The geon??s gauge bundle structure is expected to have an imprint in the Hawking-Unruh effect for quantum fields that couple to the background gauge field.     

The supersymmetric Wess-Zumino action and U(1) gauge fields

The supersymmetric effective action is constructed which when varied under gauge groups containing explicit U(1) factors reproduces the mixed gauge field contribution to the SU(N) anomaly while being U(1) invariant. It constitutes generalization of the supersymmetric Wess-Zumino action. The form of supersymmetric mixed anomaly is also discussed.     

An operatorially solved model of massless two-dimensional quantum chromodynamics

An operator solution is constructed in (1,1) dimensions to the massless quantum chromodynamics of n fermion quarks and n² ? 1 vector boson gluons with local colour SU(n) symmetry. The interacting quark field is a confined SU(n) Thirring field with zero Abelian coupling. The colour gluons are dependent Lie fields obeying the gluon-free fermionic current identity. Explicit local infinitesimal operator colour transformations (with an arbitrary coordinate-independent Lorentz vector coefficient defining the gauge) are given and the requirement of proper colour covariance linked to the vanishing of the coloured quark source currents and hence to the absence of coloured quark-composite states. The status of Noether's theorem is also clarified.     

Higgs and W mass on the lattice at strong gauge coupling

At infinite gauge coupling the gauge fields in the fundamental lattice SU(N) Higgs model can be integrated out exactly. In the resulting effective theory of the radial Higgs field we derive a string -like correlation function that represents the leading behavior of the W two-point function at small β. For large N we then compute the W-mass and the Higgs mass. These analytical results are qualitatively similar to what has been found in Monte Carlo simulations of the SU(2) model.     

Non-abelian traveling wave solutions for massless QCD2

The field equations for quantum chromodynamics in 1 + 1 dimensions (QCD₂) with massless fermions are shown to admit classical non-abelian traveling wave solutions. In this case, the field equations reduce to the linear Frenet-Serret equations for a curve in the three-space corresponding to an SU(2) subalgebra of the SU(N) gauge group.     

Monte Carlo simulation of SU(2) gauge theory with fermions on a four-dimensional lattice

After integration over the fermions in an SU(2) lattice gauge theory, the effective fermionic action may be expressed as a sum over all possible closed gauge field loops with corresponding weight factors. We approximate this sum and perform a Monte Carlo simulation of a coupled fermion-gauge system on a 4⁴ lattice. We compare our results for 〈S_eff〉 and $\text{〈}\text{ψ}\text{ψ〉}$ for different values of the gauge field coupling β and fermion coupling κ with the free fermion theory on a lattice. 〈S_eff〉 turns out to be quite small for $\text{κ?}\text{1}\text{8}$.     

Mixing of leptonic number in a general SU(2)L ⊗ U(1) ⊗ SU(2)R model

We discuss a general leptonic model based on the SU(2)_L ? U(1) ? SU(2)_R gauge group and we present general results for the ? → ?′ γ and ν? → ν?′γ processes, which can be used for any model based on the SU(2)_L ? U(1) ? SU(2)_R gauge group or on any of its subgroups. The predictions of the μ → eγ branching ratio and of the neutrino lifetime for various models discussed in the literature are reviewed. The main results are summarized in tables.     

Exact analysis of Coulomb gauge vacuum degeneracies in (2 + 1) dimensions

The solutions of the two-dimensional euclidean σ-model provide an infinite number of pure gauge field configurations satisfying the Coulomb gauge condition, in (2 + 1) dimensions. For vacuum gauge fields associated with finite action instanton solutions of the σ-model, we find that the winding number n configuration leads to n negative eigenvalues for the ghost operator, up to a finite calculable degeneracy.     

Z(N) topological excitations in Yang-Mills theories: duality and confinement

We investigate the properties of Z(N) topological excitations in Wilson's lattice formulation of SU(N) Yang-Mills theories. We exhibit the Z(N) topological excitations as exact classical solutions on the lattice. After giving detailed qualitative discussions about the Z(N) excitations and their relevance to confinement, we investigate the Z(N) lattice gauge theories with the Wilson action and show that Z(2), Z(3) and Z(4) models are self-dual systems. (The self-duality of the Z(2) case has been known previously.) This property enables us to locate the critical points exactly in those systems under the assumption that the phase transition occurs at only one point in the coupling constant space. We then derive the effective action for the Z(N) topological excitations in the lattice SU(N) Yang-Mills theories in the steepest descent approximation. The critical coupling constants in the SU(N) models corresponding to the phase transition caused by the Z(N) excitations are estimated by using the information on the Z(N) models with the Wilson action. It is quite probable that the estimated value $\text{g}{}_{\mathrm{<mtext>r</mtext>}}{}^2\text{/4π}{}^2\text{～}\text{1}\text{31}$ (for SU(3)) is an upper bound. This indicates that the Wilson model of the SU(3) gauge field can be effective action of the QCD gluons which exhibit permanent quark confinement and, at the same time, freedom up to the distance characterized by the energy, at least, ～1 TeV.     

Four-dimensional σ-model on quaternionic projective space

A four-dimensional σ-model based on the quaternionic projective space is constructed. The model possesses SU(2) gauge invariance and has one-instanton solutions analogous to those in the CPⁿ model in D=2.     

On inflation in the heterotic superstring model

The possibility is considered of achieving inflation in the field-theory limit of the E₈ X E₈ superstring model, which is an N = 1 supergravity theory possessing a “no-scale” SU(n, 1)/SU(n) × U(1) structure. It is shown that neither type I inflation (due to higher-derivative terms O(R²)), nor inflation due to a SUSY-breaking gaugino-condensation potential, is possible, essentially because of the absence of free dimensionless parameters. Kaluza-Klein type inflation is ruled out because the internal space is Ricci flat. The occurence of type II inflation (due to some gauge singlet “inflation” field φ) depends upon the form of the superpotential F and of the Kähler potential G, but this also seems not to be possible, unless the >SU(n, 1) symmetry can be broken in a particular way. Hence, some new type of compactification scheme may be called for, or a different type of inflation.     

Compactification of Einstein-Yang-Mills theories on CPn

We study compactification of Einstein-Yang-Mills theories in 2n + 4 dimensions on the manifold CP_n, with a classical gauge field that is equal to the spin connection. The complete boson fluctuation spectrum is calculated and no tachyons, ghosts or massless scalars are found for the minimal Yang-Mills group SU(n) × U(1). For larger groups, tachyons or massless scalars may appear.     

SU(2) ⊗ U(1) gauge theories of the generalized σ model for π0, η, η' → γγ decays

By embedding the chiral current-mixing gauge theories in the SU(2)_L ? SU(2)_R generalized σ model, it is shown that the correct sign and magnitude for π⁰ → γγ decay, as well as the SU(3) relation of π⁰, η, η' → γγ decays can be obtained within the framework of SU(2) ? U(1) gauge theories of weak and electromagnetic interactions.     

Generalised actions for lattice gauge models

We consider simple modifications of the conventional Wilson action for lattice gauge theory. An SU(2) action is defined on “plaquettes” of 2×1 links. It is found to possess phase transitions in three- and four-dimensional realisations of the model. A similar model with gauge group Z(2) is also studied, and found to have two phases in three and four dimensions. We discuss the phase structure of Z(N) gauge models in four dimensions with several coupling constants and present phase diagrams for Z(4), Z(5) and Z(6).     

A visualization of the SU(2) vacuum on the lattice

Configurations of pure SU(2) gauge field theory on lattice are transformed to Landau gauge. After Fourier transformation, large momentum amplitudes are suppressed (filtered) by a variable amount, and the configurations are transformed back to x-space. Spectacular peaks in electric and magnetic field strengths are found, which share many properties with either almost pointlike instantons or with extended anti-instantons. The environment around those peaks are visualized with respect to the action, to the topological charge density, to the gauge fields and to electric and magnetic field strengths. The density of the peaks is of order 1 fm^–4, and it scales according to the string tension under a variation of the coupling constant. The evolution of the peaks under the amount of Fourier filtering is visualy compared to the evolution under cooling, and the gauge dependence of the peaks is discussed. Advantages and shortcomings of this method are discussed, with emphasis on possible strong distortions of the action and topological charge density, which become gauge dependent. Finally, I compare the character of the SU(2)-configurations to those of noncompact abelian theory.     

Finite matrix models with continuous local gauge invariance

We construct a hamiltonian lattice gauge theory which possesses local SU (2) gauge invariance and yet is defined on a Hilbert space of 5-dimensional real vectors for every link. This construction does not allow for generalization to arbitrary SU(N), but a small variation of it can be generalized to an SU(N) × U(1) local gauge invariant model. The latter is solvable in simple gauge sectors leading to trivial spectra. We display these by studying a U(1) local gauge invariant model with similar characteristics.     

N = 1 complex supersymmetric theory in the harmonic superspace

The N = 1 complex supersymmetric algebra is studied using the harmonic techniques. The massless representations and the classification of their field content in terms of SU(2) n-uplets is obtained. The superspace formulation is developed and the U(1) × U(1) gauge supermultiplet is examined. Other features are discussed.