G.M. Sotkov

Modular invariance and the two-loop vanishing of the cosmological constant

Abstract With a moduli independent choice of super-Beltrami differentials, we show, by using the genus-two hyperelliptic formalism, that the requirement of modular invariance determines completely the two-loop amplitudes of the heterotic string theory for arbitrary external legs and that the cosmological constant is zero pointwise in moduli space.

Renormalization group flow for general SU(2) coset models

Abstract We show that there exists a renormalization group flow from p th to ( p - l )th model in the l th level SU (2) coset series, for p large.

Affine geometry and WN-Gravities

Abstract We demonstrate that the quantum W 3 -gravity has a cllasscal limit ( c → −∝) the geometry of the affine surfaces of constant mean curvature immersed in 3D affine space. The relations of the affine curve geometries to the (1D) W n minimal models is also discussed.

Bootstrap fusions and tricritical Potts model away from criticality

Abstract We present the analysis of the tricritical 3-state Potts model perturbed by the energy density field e=o ( 1 7 1 7 ) and the S -matrices of the (conjectured) field theory. A general scheme for solving the minimal integrable models starting from the possible bootstrap fusions is also discussed.

Fusions of Conformal Models

Abstract We show that the higher level SU(2)-coset models can be represented by the projected tensor products of the Virasoro models. We prove the modular covariance of the prescription, construct the monodromy-invariant correlation functions for arbitrary level fields and calculate some of the structure constants. Some properties of the moduli spaces of these projected tensor product models are discussed.

Extrinsic geometry of strings and W-gravities

We demonstrate that specific noncritical string models with extrinsic geometrical degrees of freedom in dcl = 3, 4, 6 are equivalent to the WSO(dcl) gravities.

Minimal models on hyperelliptic surfaces

Abstract The Virasoro minimal models on the hyperelliptic surfaces are mapped into the specific models on the branched sphere. The latter are described by a generalized Coulomb gas representation. The partition functions of the models on the Z 2-surfaces (g⩾1) are constructed in terms of the correlation functions of fields from the twisted sector of the branched sphere models.

Fine structure of the supersymmetric operator product expansion algebras

Abstract A detailed discussion of the Ramond sector of the superconformal minimal models (m.m.) in terms of the Coulomb gas representation is given. The basic elements of this construction, vertices and screening operators, are written in terms of the critical Ising variables (order-disorder parameter fields, free Majorana fermion) and of a free dimensionless field. The fusion rules in all the sectors of the superconformal m.m. and the explicit expression for the structure constants of the operator product expansion are obtained. The Ramond fields are used to describe the Z 2 odd sector of the tricritical Ising model and the critical Ashkin-Teller model.

Ramond Sector of the Supersymmetric Minimal Models

Abstract A Coulomb gas representation for the Ramond sectors of the N = 1 supersymmetric models is constructed. The fusion rules and the 4-point functions for the Ramond fields are calculated explicitly by this method and used to describe the Z 2 odd sectors of the tricritical Ising model and of the critical Kosterlitz-Thouless XY model.

Fusion rules, four-point functions and discrete symmetries of N = 2 superconformal models

Abstract Fusion rules, structure constants and four-point functions for all the fields of N = 2 superconformal minimal models ( c ⩽ 3) are derived. It is shown that the additional Z p +2 symmetries of these models are generated by specific N = 2 superfields which close the N = 2 superparafermionic algebra. General results are applied to the four- and three-generation Gepner tensor product models and the allowed Yukawa couplings are found.