International Journal of Modern Physics A

Particular deformations of 2-D conformal field theory lead to integrable massive quantum field theories. These can be characterized by the relativistic scattering data. We propose a general scheme for classifying the elastic nondegenerate S-matrix in (1 + 1) dimensions starting from the possible boot-strap processes and the spins of the conserved currents. Their identification with the S-matrix coming from the Toda field theory is analyzed. We discuss both cases of Toda field theory constructed with the simply-laced Dynkin diagrams and the nonsimply-laced ones. We present the results of the perturbative analysis and their geometrical interpretations.

We show that the operator content of a conformal field theory defined on surfaces with boundaries and crosscaps is more restricted when the periodic sector is described by nondiagonal modular invariants than in the case of diagonal modular invariants. By tensoring, the restrictions can be alleviated, leading to a rich structure. Such constructions are useful, for example, in lower-dimensional open superstring models.

We derived a general formula for the action for O(3)-invariant tunneling processes at false vacuum decay in general relativity. A general classification of bubble shell Euclidean trajectories is elaborated and explicit expressions for bounces for a number of processes like spontaneous vacuum creation of a double bubble (in particular in the vicinity of a black hole), subbarrier creation of the Einstein-Rosen bridge, tunneling of a black hole to the state of a wormhole, creation from nothing of two Minkowski worlds connected by a shell, etc., are given.

The higher-dimensional Einstein vacuum equation with Λ-term is shown to be conformally equivalent to the four-dimensional field equation of scale-invariant fourth-order gravity. This holds for a general warped product between space-time and internal space of arbitrary dimension m which turns out to be an Einstein space. (The limit m → ∞ makes sense!)

Thus, the results concerning the attractor property of the power-law inflationary solution derived for fourth-order gravity hold for the Kaluza-Klein model, too.

The conformal relation between scale-invariant fourth-order gravity and Kaluza-Klein models as derived in the preceding paper (I) is applied to Friedmann cosmological models. Especially, the result that power-law inflation is an attractor solution can be carried over, but the conformal transformation brings power-law inflation to de Sitter-like exponential inflation, or power-law inflation a ≈ t.

The results depend essentially on the dimension of the internal space.

We discuss possible approaches to the investigation of anomalous processes with fermion number nonconservation occurring in the hot early Universe. A real-time numerical technique for studying the ground state of gauge theories at high temperatures is developed. This problem is relevant to the scenario of electroweak BAU generation and some other topics. We present the results of real-time simulations of the Abelian Higgs model in (1 + 1) dimensions.

We show that there is a useful regularization of quantum field theories obtained by replacing invariant integration over Euclidean momentum space by invariant integration over a quantum group of q-momentum space. We exhibit quantites that are made finite as q ≠ 1 but diverge as the regulator is removed by q → 1.

We show how to handle together constraints coming from associativity, modular invariance and analyticity in RCFT's. In particular, looking at the theories with three operators we classify fusion rule algebras, central charges and conformal weights fulfilling such constraints. We also show that all allowed theories with three operators are algebraic.

A general method for constructing interesting topological gauge theories in arbitrary dimensions is presented. The basic framework upon which these models are built is given by the geometrical data of the "universal bundle with connection" of Atiyah and Singer. The models considered include theories which represent the moduli spaces of flat connections and solutions to the Yang-Mills equations. The former theories correspond to supersymmetric versions of the recently introduced BF systems. In all cases we show explicitly that the quantization can be carried out through the construction of an off-shell nilpotent BRST operator, thus guaranteeing the metric independence of these models.

The N = 2 super-Kac-Moody algebra is defined as the algebra corresponding to an N = 2 superloop group. Using the method of coadjoint orbits, which is explained, an action is derived which has the N = 2 super-Kac-Moody algebra as its Poisson bracket algebra and is invariant under the N = 2 superloop group. It is invariant under N = 2 superconformal transformations. This action is thus the generalization of the WZW model to (2,0) superspace. We study the relation to the known WZW model in (1,0) superspace after imposing a constraint on the (2,0) superfield.