A. Sevrin

THE FULL STRUCTURE OF THE SUPER W3 ALGEBRA

We investigate a supersymmetric extension of the W3 algebra, which is common to a c=4 free fermion model and to the generic c<4 supersymmetric coset models based on at level (3, m). By using the so-called character technique, we identify a set of eight generating supercurrents of this algebra. For m=1, corresponding to c=10/7, the algebra reduces to the “minimal” super W3 algebra, which has been studied previously.

A Derivation of the BRST Operator for Non-Critical W Strings

Abstract We derive the recently proposed BRST change for non-critical W strings from a lagrangian approach. The basic observation is that, despite appearances, the combination of two classical “matter” and “Toda” w 3 systems leads to a closed modified gauge algebra, which is of the so-called soft type. Based on these observations, a novel way to construct critical W 3 strings is given.

Extensions of the Virasoro algebra and gauged WZW models

Abstract To any non-trivial embedding of sl(2) in a (super) Lie algebra, one can associate an extension of the Virasoro algebra. We realize the extended Virasoro algebra in terms of a WZW model in which a chiral, solvable group is gauged, the gauge group being determined by the sl(2) embedding. The resulting BRST cohomology is computed and the field content of the extended Virasoro algebra is determined. The closure of the extended Virasoro algebra is shown. Applications such as the quantum Miura transformation and the effective action of the associated extended gravity theory are discussed.

Properties of covariant W gravity

We present the beginnings of a new consistent gauge theory with spin 2 and spin 3 gauge fields in two dimensions. It is based on a nonlinear Lie algebra, whose “gauging” is discussed in detail. (The present treatment of the gauge sector is expanded as compared to [3]). For the coupling to matter, we introduce the concept of a “nested covariant derivative”, and we obtain an invariant action by solving a functional integrability condition. It reads

Induced and effective gravity theories in D = 2☆

Abstract As a preparation for the study of arbitrary extensions of d = 2 gravity we present a detailed investigation of SO(N) supergravity. Induced d = 2, SO(N) supergravity is constructed by gauging a chiral, nilpotent subgroup of the OSp (N|2) Wess-Zumino-Witten model. In order to get a gauge-invariant theory with the correct number of degrees of freedom, we need to introduce N free fermions. From this we derive an all-order expression for the effective action. Reality of the coupling constant imposes the usual restrictions on c for N = 0 and 1. No such restrictions appear for N ⩾ 2. For N = 2, 3, and 4, no renormalizations of the coupling constant beyond one-loop occur. Also, in the effective N = 4 gravity based upon a linear N = 4 superconformal algebra, there is no renormalization at all, i.e. the quantum for theories with extended supersymmetries. Arbitrary (super) extensions of d = 2 gravity for theories with extended supersymmetries. Arbitrary (super) extensions of d = 2 gravity are then analyzed. The induced theory is represented by a WZW model for which a chiral, solvable group is gauged. From this, we obtain the effective action. All order expressions for both the coupling constant renormalization and the wave-function renormalization are given. From this we classify all extensions of d = 2 gravity for which the coupling constant gets at most a one-loop renormalization. As an application of the general strategy, N = 4 theories based on D(2, 1, α) and SU (1, 1|2), all WA gravities and the N = 2 Wn models are treated in some detail.

TOWARDS A SUPERSYMMETRIC NON-ABELIAN BORN-INFELD THEORY

We define an iterative procedure to obtain a non-abelian generalization of the Born-Infeld action. This construction is made possible by the use of the severe restrictions imposed by kappa-symmetry. We have calculated all bosonic terms in the action up to terms quartic in the Yang-Mills field strength and all fermion bilinear terms up to terms cubic in the field strength. Already at this order the fermionic terms do not satisfy the symmetric trace-prescription.

RELATION BETWEEN LINEAR AND NONLINEAR N = 3,4 SUPERGRAVITY THEORIES

The effective actions for d=2, N=3, 4 chiral supergravities with a linear and a nonlinear gauge algebra are related to each other by a quantum reduction; the latter is obtained from the former by putting quantum currents equal to zero. This implies that the renormalization factors for the quantum actions are identical.

Regularisation of non-local actions in two-dimensional field theories

Abstract Taking the induced action for gauge fields coupled to affine currents as an example, we show how loop calculations in non-local two-dimensional field theories can be regulated. Our regularisation method for one loop is based on the method of Pauli and Villars. We use it to calculate the renormalisation factors for the corresponding effective actions, clearing up some discrepancies in the literature. In particular, it will be shown explicitly that vector gauge transformation invariance and Haar invariance of functional integral measures impose different requirements, but they are related by a counterterm (which is local in terms of group variables). For higher loops, we use the method of covariant derivatives combined with Pauli-Villars to argue that the one-loop result remains unaltered.

Quantum gauging from classical gauging of nonlinear algebras

We extend our previous theory of the gauging of classical quadratically nonlinear algebras without a central charge but with a coset structure to the quantum level. Inserting the minimal anomalies into the classical transformation rules of the currents introduces further quantum corrections to the classical transformation rules of the gauge fields and currents which additively renormalize the structure constants. The corresponding Ward identities are the [ital c][r arrow][infinity] limit of the full quantum Ward identities, and reveal that the [ital c][r arrow][infinity] limit of the quantum gauge algebra closes on fields and currents. Two examples are given.

Relation between linear and nonlinear [ital N]=3,4 supergravity theories

The effective actions for d=2, N=3, 4 chiral supergravities with a linear and a nonlinear gauge algebra are related to each other by a quantum reduction; the latter is obtained from the former by putting quantum currents equal to zero. This implies that the renormalization factors for the quantum actions are identical.