Peter Bouwknegt

W symmetry in conformal field theory

Abstract We review various aspects of W algebra symmetry in two-dimensional conformal field theory and string theory. We pay particular attention to the construction of W algebras through the quantum Drinfeld-Sokolov reduction and through the coset construction.

BRST analysis of physical states for 2D gravity coupled toc≦1 matter

We consider 2D gravity coupled toc≦1 conformal matter in the conformal gauge. The Liouville system is represented by a free scalar field,φL, with background charge such that the BRST operator imposing reparametrization invariance is nilpotent. We compute the cohomology of this BRST charge on the product of the Fock space ofφL with those of the ghosts and one other free scalar field,φM representing the matter system. From this calculation the physical states of the full theory are determined. For thec<1 case the further projection from the Fock space ofφM to the irreducible representation, using Felders resolution, reproduces the results of Lian and Zuckerman.

Spinon bases, Yangian symmetry and fermionic representations of Virasoro characters in conformal field theory

Abstract We study the description of the SU (2), level k = 1, Wess-Zumino-Witten conformal field theory in terms of the modes of the spin- 1 2 affine primary field φ α . These are shown to satisfy generalized ‘canonical commutations relations’, which we use to construct a basis of Hilbert space in terms of representations of the Yangian Y ( sl 2 ). Using this description, we explicitly derive so-called ‘fermionic representations’ of the Virasoro characters, which were first conjectured by R. Kedem, T. Klassen, B. McCoy and E. Melzer [Phys. Lett. B 307 (1993) 68, and references therein]. We point out that similar results are expected for a wide class of rational conformal field theories.

Spinon basis for higher level SU(2) WZW models

We propose a spinon basis for the integrable highest weight modules of sl2 at levels k ≥ 1, and discuss the underlying Yangian symmetry. Evaluating the characters in this spinon basis provides new quasi-particle type expressions for the characters of these integrable modules, and explicitly exhibits the structure of an RSOS times a Yangian part, known e.g. from S-matrix results. We briefly discuss generalizations to other groups and more general conformal field theories.

Ground ring for the two-dimensional NSR string

We discuss the BSRT quantization of two-dimensional N = 1 supergravity coupled to super-conformal matter with c ⩽ 1 in the conformal gauge. The physical states are computed as BRST cohomology. In particular, we consider the ring structure and associated symmetry algebra for the two-dimensional superstring (c = 1).We discuss the BSRT quantization of 2D

Fock space resolutions of the Virasoro highest weight modules with c <= 1

N=1

Semi-infinite cohomology ofW-algebras

supergravity coupled to superconformal matter with

Semi-infinite cohomology in conformal field theory and 2D gravity

\hat{c} \leq 1

BRST Analysis of Physical States for 2D (Super) Gravity Coupled to (Super) Conformal Matter

in the conformal gauge. The physical states are computed as BRST cohomology. In particular, we consider the ring structure and associated symmetry algebra for the 2D superstring (

On the W-Gravity Spectrum and Its G-Structure

\hat{c} = 1