International Journal of Modern Physics A

The problem of dynamic electroweak symmetry breaking (DEWSB) is reviewed. The emphasis is on the consideration of the dynamics of spinless tight bound states which can be an essential ingredient of the DEWSB scenario.

The massless states in 27 and of E₆ are constructed for the ten N=2 superconformal coset theories based on a Hermitian symmetric space for which the gauge group is E₆×E₈ with no extra U(1) factors.

The structure of the state space in the BRST-quantization is considered and the connection between different approaches to the proof of the positive-definiteness of the metric on the physical state space is established. The correspondence between different expressions for the BRST-charge, quadratic in fields, is obtained. The relation between different representations of the BRST-algebra is found.

It is shown that the gauge-invariant description of higher spin fields requires a nonlocal generalisation of the theory. Nonlocal gauge-invariant action functionals for spin 3/2 field and tensor spin 2 field in curved space are constructed.

The multiply charmed baryons have a very interesting spectroscopy and provide a unique laboratory for studying the strong interaction dynamics that bind quarks into hadrons. We wish to point out that the weak decay of these hadrons is also interesting and examine the flavor SU(3) predictions for their nonleptonic and semileptonic decay.

A perturbative technique for finding solutions of the Virasoro master equation is developed. Isolated solutions as well as solutions with continuous parameters are discovered. The cases of SU(2) and SU(3) are discussed in detail.

We propose an off-shell extension of the closed bosonic string scattering amplitudes as functional integrals over bordered Riemann surfaces. The tree level off-shell N-scalars amplitude is handled with the help of Schottky groups and the Burnside θ-series. Using these tools and the asymptotic behaviour of the partition function at the boundary of the moduli space, we show that the off-shell amplitudes exhibit the tachyon mass-shell poles in the external momenta. In addition, their residues are shown to be the semi-off-shell amplitudes and the well-known Koba-Nielsen amplitudes.

We discuss some nonperturbative aspects of the correspondence between N=2 Landau-Ginzburg orbifolds and Calabi-Yau σ-models. We suggest that the correct framework is Deligne’s theory of mixed Hodge structures (closely related to catastrophe theory). We derive a general topological formula for the chiral ring OPE coefficients of any Landau-Ginzburg model, including the absolute normalization. This follows from the identification of spectral flow with Grothendieck’s local duality. Wherever the LG model has a CY interpretation, its OPE coefficients are equal to those of the σ-model as given by intersection theory, including normalization. We discuss at length the tricky case of a number of LG fields greater than c/3+2, presenting explicit examples. In passing, we get many results about the geometry of moduli spaces for such conformal theories. We explain the beautiful algebraic geometry connected with a remarkable model pointed out by Vafa, and its relations with moduli space geometry.

We show how the vacuum expectation value of the Wilson loop of the trivial knot in the left-regular representation in a Chern-Simons theory is basically the partition function for a quantum particle confined to a certain bounded region (namely, an alcove of the gauge group Lie algebra). For example, for su(3) the particle is confined to an equilateral triangle. The result follows from mathematical work on the category-theoretic rank of quantum groups obtained in a previous paper. In the present paper we give the details of the physical interpretation and discuss the implications. In particular, both these physical systems are connected with number theory.

Gauge theories based upon a direct product G₁×G₂ of two gauge theories are considered. We examine the general features of models where the theory based upon G₁ is asymptotically finite and that based upon G₂ is asymptotically free. A simple model in which the product theory is asymptotically finite is presented.

Following the recent construction of unitary irrational central charge on compact affine g, we begin a series of papers to report further solutions of the Virasoro master equation and related topics in irrational conformal field theory. This paper completes the maximal-symmetric subansatz by obtaining the three-parameter unitary irrational construction , which contains the known solution and involves a root of a root generically.