Spin and mass content of linearized Poincaré gauge theories

A unified gauge theory of massless and massive spin-2 fields is of considerable current interest. The Poincaré gauge theories with quadratic Lagrangian are linearized, and the conditions on the parameters are found which will lead to viable linear theories with massive gauge particles. As well as the 2⁺ massless gravitons coming from the translational gauge potential, the rotational gauge potentials, in the linearized limit, give rise to 2⁺ and 2⁻ particles of equal mass, as well as a massive pseudoscalar.     

Strong coupling expansions for the mass gap in lattice gauge theories

We derive strong coupling expansions for the mass gap in euclidean lattice gauge theories in any space-time dimension. For gauge groups SU(2), SU(3), Z₂ and Z₃ the series are calculated up to order g^?16. They are used to get rough estimates for the lowest glueball mass in continuum SU(2) and SU(3) gauge theories, assuming a sudden crossover from strong to weak coupling behaviour in the lattice theory.     

Noncommutative Instantons Revisited

We find a new gauge in which U(1) noncommutative instantons are explicitly non-singular on noncommutative R ⁴. We also present a pedagogical introduction into noncommutative gauge theories.     

Improved methods for supergraphs

We introduce some new techniques into superfield perturbation theory which allow considerable simplifications in calculations. As a result, we show that all contributions to the effective action can be written as integrals over a single d⁴θ. We also give the background group field formalism for supersymmetric non-abelian gauge theories. To illustrate our methods, we give examples of loop calculations: in particular, we show that in O(4) extended supersymmetric non-abelian gauge theories all one-loop propagator corrections cancel identically (both infinite and finite parts) and that these theories, at one loop, are finite and have no renormalizations (in the Fermi-Feynman gauge).     

Strong-coupling expansions for the off-axis glueball masses

Strong-coupling expansions, up to order g^?4, for the off-axis glueball masses are developed in four-dimensional spacetime for lattice gauge theories with gauge groups SU(2), SU(3), Z₂, Z₃. Glueball mass spectra for the states 0⁺⁺, 2⁺⁺, 1^+? are obtained. Restoration of Lorentz invariance is discussed.     

The Parametrization Invariant and Gauge Invariant Effective Actions in Quantum Field Theory

The review of formulation and methods of calculation of the parametrization and gauge invariant effective actions in quantum field theory is given. As an example the Vilkovisky-De Witt Effective action (EA) is studied (this EA is a natural representative of gauge and parametrization invariant EA's). The examples where the use of the standard EA leads to the ambiguity are demonstrated. This happens as the result of dependence of the standard EA upon the choice of gauge condition. These examples are as follows: Coleman-Weinberg potential in the finite theories and symmetry breaking, EA in quantum gravity with matter and d = 5 gauged supergravity, the possibility of spontaneous supersymmetry breaking in N = 1 supergravity and the spontaneous compactification in the multidimensional R²-gravity. In all these cases the one-loop Vilkovisky-De Witt EA is found and therefore the problem of gauge dependence of EA is solved. The dependence of standard EA of composite fields upon the gauge is studied for the general gauge theories. The class of gauge and parametrization invariant EA's of the composite fields is offered.     

Physics prospects at a linear e + e − collider

The talk described the prospects of studying standard model parameters as well as scenarios beyond the standard model, like the minimal supersymmetric standard model, theories with extra dimensions and theories with extra neutral gauge bosons, at a future linear e ⁺ e ⁻ collider.     

Hidden symmetry and the possibility of spin-zero leptons

Hidden in a class of gauge theories is a global symmetry which is only apparent after spontaneous breakdown of the local gauge symmetry. A particularly interesting outcome of this hidden symmetry is the possibility of spin-zero leptons, which could be responsible for the anomalous eμ events seen in e⁺e^?annihilation, as recently proposed by Ma, Pakvassa and Tuan.     

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.     

Gauge coupling renormalisation with several U(1) factors

We examine the renormalisation of gauge coupling constants in theories with a G × U(1)^N gauge group (which appears to be the gauge symmetry of many possible superstring vacua). In general, the abelian gauge bosons mix among themselves, so a correct renormalisation requires including this mixing in the evolution of the gauge couplings. We present general results and note that the mixing is scale independent to all orders if the renormalization group trajectory passes through a unification point. We discuss the cases of one loop and two loops explicitly. An example, based on a possible superstring-inspired model, is given.     

Quantum vortex strings: A review

The quantum worldsheet dynamics of vortex strings contains information about the 4d non-Abelian gauge theory in which the string lives. Here I tell this story. The string worldsheet theory is typically some variant of the CP^N-1 sigma-model, describing the orientation of the string in a U(N) gauge group. Qualitative parallels between 2d sigma-models and 4d non-Abelian gauge theories have been known since the 1970s. The vortex string provides a quantitative link between the two. In 4d theories with N=2 supersymmetry, the exact BPS spectrum of the worldsheet coincides with the bulk spectrum in 4d. Moreover, by tuning parameters, the CP^N-1 sigma-model can be coaxed to flow to an interacting conformal fixed point which is related to the 4d Argyres-Douglas fixed point. For theories with N=1 supersymmetry, the worldsheet theory suffers dynamical supersymmetry breaking and, more interestingly, supersymmetry restoration, in a way which captures the physics of Seiberg’s quantum deformed moduli space.     

Abelian gauge theories on homogeneous spaces

An algebraic technique of separation of gauge modes in Abelian gauge theories on homogeneous spaces is proposed. An effective potential for the Maxwell-Chern-Simons theory on S ³ is calculated. A generalization of the Chern-Simons action is suggested and analyzed with the example of SU(3)/U(1) X U(1).     

Gauge theory onR×S 3 topology

A model for gauge theories over a compact Lie group is described using R × S³ as background space. The U(1) and SU(2) gauge theories are considered as particular examples, and a comparison with other results is given. Our results differ from those of Carmeli and MalinFound. Phys. 16, 791 (1986);17, 193 (1987)] by a supplementary term in the curvature tensor due to the noncommutativity of derivatives used on R × S³ space. Some observations about supersymmetry and gravity on R × S³ space are also given.     

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.     

Dimensional regularisation in the presence of large background fields

The method of dimensional regularisation is introduced and discussed in detail for the case of quantum field theories with large (i.e., not infinitesimal) classical background fields. Examples considered are the φ⁴-theory on four-dimensional compact curved spaces as well as Yang-Mills gauge theories on S⁴ with an arbitrary multi-instanton background field.     

Characteristic cohomology ofp-form gauge theories

The characteristic cohomologyH ^k _char(d) for an arbitrary set of freep-form gauge fields is explicitly worked out in all form degreesk < n — 1, wheren is the spacetime dimension. It is shown that this cohomology is finite-dimensional and completely generated by the forms dual to the field strengths. The gauge invariant characteristic cohomology is also computed. The results are extended to interactingp-form gauge theories with gauge invariant interactions. Implications for the BRST cohomology are mentioned.     

On the energy-momentum tensor in gauge field theories

The energy-momentum tensor in spontaneously broken non-Abelian gauge field theories is studied. The motivation is to show that recent results on the finiteness and gauge independence of S-matrix elements in gauge theories extends to observable amplitudes for transitions in a gravitational field. Path integral methods and dimensional regularization are used throughout. Green's functions Γ_μν^(j)(q; p₁,…,p_j) involving the energy-momentum tensor and j particle fields are proved finite to all orders in perturbation theory to zero and first order in q, and finite to one loop order for general q. Amputated Green's functions of the energy momentum tensor are proved to be gauge independent on mass shell.     

Renormalization of a gauge theory in a nonlinear gauge

We discuss renormalization of an O(3) gauge model with the gauge fixing term given by ℒ_g.f.=-1/ζ|(∂_μ-igA ₃ ^μ )W ^+μ|²-(1/2α)(∂A ³)². We utilize earlier results on the general theory of renormalization of gauge theories in quadratic gauges to prove multiplicative renormalizability of the theory together with a subtractive renormalization of gauge fixing and ghost terms. We show that this model has a double BRS invariance and that it is preserved under renormalization.