Modern Physics Letters A

An effective sigma model describing behavior of the 3-D rigid string with a θ-term at θ=π is proposed. It contains nonperturbative corrections resulting from summation over different genera of the 2-D surfaces. The effective theory is the SU(2) WZW model coupled to the Nambu-Goto action. RG analysis shows the existence of an ir fixed point at which the normal to the surface has long range correlations. A similar model can describe critical behavior of the 3-D YM fields or the Ising model.

In a recent paper Dargis and Mathieu introduced integrodifferential odd flows for the supersymmetric KdV equation. These flows are obtained from the nonlocal conservation laws associated with the fourth root of its Lax operator. In this note I show that only half of these flows are of the standard Lax form, while the remaining half provide us with Hamiltonians for an SKdV-type reduction of a new supersymmetric hierarchy. This new hierarchy is shown to be closely related to the Jacobian supersymmetric KP-hierarchy of Mulase and Rabin. A detailed study of the algebra of additional symmetries of this new hierarchy reveals that it is isomorphic to the super-W_1+∞ algebra, thus making it a candidate for a possible interrelationship between superintegrability and two-dimensional supergravity.

The kinematic of SL(2, ℝ) Yang-Mills theory on a circle is considered, for reasons that are spelt out. The gauge transformations exhibit hyperbolic fixed points, and this results in a physical configuration space with a non-Hausdorff “network” topology. The ambiguity encountered in canonical quantization is then much more pronounced than in the compact case and cannot be resolved through the kind of appeal made to group theory in that case.

We show that the action of self-dual supersymmetric Yang-Mills theory in four dimensions, which describes the consistent massless background fields for N=2 superstring, generates the actions for N=1 and N=2 supersymmetric non-Abelian Chern-Simons theories in three dimensions after some dimensional reductions. Since the latters play important roles for supersymmetric integrable models, this result indicates the fundamental significance of the N=2 superstring theory controlling (possibly all) supersymmetric integrable models in lower dimensions.

The connection between Z_n×Z_n symmetric solutions of the star-triangle equation and solutions of the Yang-Baxter equation is used to construct a new set of n-state (for any odd n) two-parameter solution of the Yang-Baxter equation. For n=3 the solution was found by M. Jimbo and T. Miwa in 1985.

A unified and systematic scheme for construction of differential operator realization of any irreducible representation of sl(n) is developed. The q-analog of this unified scheme is used to construct q-difference operator realization of any irreducible representation of U_q(sl(n)). Explicit results for U_q(sl(2)), U_q(sl(3)) and U_q(sl(n)) are given.

It is shown that Weyl spinors in Minkowski space are isomorphic to primary fields of half-integer conformal weights. This yields representations of fermionic two-point functions in terms of correlators of primary fields with a factorized transformation behavior under the Lorentz group. As an application we determine the general structure of the corresponding Lorentz covariant correlators by methods similar to that employed in conformal field theory to determine two- and three-point functions of primary fields. In particular, the chiral symmetry breaking terms resemble fermionic two-point functions of 2-D CFT up to a function of the product of momenta.

Generalized quons interpolating between Bose, Fermi, para-Bose, para-Fermi and anyonic statistics are proposed. They follow from the R-matrix approach to deformed associative algebras. It is proved that generalized quons have the same main properties as quons. A new result for the number operator is presented and some physical features of generalized quons are discussed in the limit .

High energy electroweak data, including the recent measurement of M_top is analyzed within the basic framework of the standard model. While the experimentally measured value of implies a low value of M_top, the rest of the data demands a much higher value. Estimates of M_Higgs within the SM framework including and excluding this R_b measurement are given. Next this discrepancy is expressed in terms of a new parameter, , the excess production compared to that expected from a SM fit. This parameter is determined to be (9.4 to 12.8) ± 5.0 MeV, implying an excess of over 10 000 events in each LEP experiment after the 1993 data is fully analyzed. The origin of these events could be non-minimal Higgs pair production which should be thoroughly searched for in the full data sample of ~2×10⁶ events per LEP experiment. Unless this discrepancy eventually turns out to be a fluctuation one may be witnessing at LEP the advent of physics beyond the standard model.

The analog of the string equation which specifies the partition function of c=1 string with a compactification radius β∈Z_≥1 is described in the framework of the Toda lattice hierarchy.