International Journal of Modern Physics A

Of the many ingredients of the Standard Model that are relevant to the analysis of CP asymmetries in B⁰ decays, some are likely to hold even beyond the Standard Model while others are sensitive to new physics. Consequently, certain predictions are maintained while others may show dramatic deviations from the Standard Model. Many classes of models may show clear signatures when the asymmetries are measured: four quark generations, Z-mediated flavor-changing neutral currents, supersymmetry and “real superweak” models. On the other hand, models of left-right symmetry and multi-Higgs sectors with natural flavor conservation are unlikely to modify the Standard Model predictions.

It is proposed that a classically conserved current may not be conserved in quantum theory due to singular configurations in the path integral. This is illustrated in the (2+1)-dimensional O(3) nonlinear sigma model with lattice regularization. The current here is that of the topological charge density of “Skyrmions”. On the lattice the current is always “anomalous”, due to the existence of Dirac monopoles. The reason is that the world line of a Skyrmion can be regarded as a Dirac string (in a particular gauge), which is terminated by a monopole. Monte-Carlo simulations indicate that, in the continuum limit, current conservation obtains in a weak-coupling phase, in which monopole and anti-monopoles form bound states that disappear upon coarse-graining; but the anomaly persists in a strong-coupling phase, in which the above-mentioned bound states dissociate into a plasma. In the plasma phase rotational invariance will be broken in the presence of a “Hopf term” in the action.

In previous articles classical gauge theory was studied with a matrix algebra as an additional noncommutative factor in the algebra of classical observables. The extra derivations permitted a unification in a common multiplet of a set of Higgs fields with the gauge potentials. In the present article the algebra of derivations is modified in order to obtain a theory which is closer to a realistic physical model.

As a first step towards a classification of the heterotic superstring solutions in the fermionic approach, we study a class of solutions characterized by complex fermions with Z_N boundary conditions. The same solutions can be obtained by an equivalent modular invariant system of real fermions with Z₂ boundary conditions. The proof is supplied by Riemann identities for Jacobi Θ-functions that we derive. The patterns of the gauge groups of the D-dimensional solutions are determined for 4≤D≤10, and their uniqueness in ten dimensions is checked for the different Z_N boundary conditions. A construction of the E₈×E₈ supersymmetric solution based on nine complex fermions with Z₃ periodicity is exhibited.

The classical mechanics of a scalar particle interacting with a Chern-Simons field in the (2+1)-dimensional space-time has been considered. The geometric quantization of this system does not lead to particle statistics transmutation. This result is in apparent contradiction with the statement of Ref. 1.

The equations of motion for the massless modes of the closed bosonic string are obtained in the adiabatic approximation from the requirement of the vanishing of the curvature of appropriate vector bundles over the space of complex structures Diff S¹/S¹. This vanishing is required for physical states to be independent of string parametrization.

We derive several results pertaining to anyonic superconductivity as described by a Chern-Simons field theory. (1) The renormalized Chern-Simons term at finite density is shown to vanish when the renormalized coefficient at zero density takes values Ne²/2π. This is the field-theoretical requirement to have a massless pole in the current-current correlator. We can then show that in the Chern-Simons description a system of charged anyons at zero temperature is a superconductor. This result is shown to hold to all orders in perturbation theory by generalizing a nonrenormalization theorem of the zero density case. (2) At finite temperature the renormalized Chern-Simons term does not vanish at the one-loop perturbative level. We compute the mass of this apparent “pseudo-Goldstone mode”. We also exhibit an effect suggestive of critical behavior, for this same system, at a nonzero T_c. We discuss the possible implications of these perturbative results. (3) A low energy effective action for an anyonic superconductor is derived directly from Chern-Simons field theory. Several P and T violating effects occur.

Soliton operators of fractional spin and statistics are constructed using canonical quantization of the O(3) nonlinear sigma model with a topological Hopf action in 2+1 dimensions. The role of the Hopf term as the nontrivial holonomy of a flat connection in the configuration space is emphasized.

We study the continuum Schwinger-Dyson equations for nonperturbative two-dimensional quantum gravity coupled to various matter fields. The continuum Schwinger-Dyson equations for the one-matrix model are explicitly derived and turn out to be a formal Virasoro condition on the square root of the partition function, which is conjectured to be the τ function of the KdV hierarchy. Furthermore, we argue that general multi-matrix models are related to the W algebras and suitable reductions of KP hierarchy and its generalizations.

The S-matrices for ϕ_1,2-perturbated minimal models are shown to be connected with RSOS projections of the R-matrix. The agreement with the known particular cases (E₆, E₇, E₈, D₄) is established.

We show how the entire KdV hierarchy as well as the recursion relation between the conserved quantities can be obtained from a spin-2 flow. The relationship between this approach and the zero curvature formulation of the KdV system based on the group SL(2, R) is clarified. We show that the Boussinesq equation can be derived as a flow of the spin-3 transformations. The Boussinesq hierarchy, as well as the relevant Lenard relation, is derived from a combined flow of the spin-2 and spin-3 transformations. We have also given an independent derivation of the Lenard relation for the Boussinesq equation starting from the third order Schrödinger equation.