James G. McCarthy

Quantum group structure in the Fock space resolutions of\(\widehat{sl}(n)\) representations

AbstractWe describe a complex of Wakimoto-type Fock space modules for the affine Kac-Moody algebran

Free field realizations of WZNW models. The BRST complex and its quantum group structure

widehat{sl}(n)

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

n. The intertwining operators that build the complex are obtained from contour integrals of so-called screening operators. We show that a quantum group structure underlies the algebra of screening operators. This observation greatly facilitates the explicit determination of the intertwiners. We conjecture that the complex provides a resolution of an irreducible highest weight module in terms of Fock spaces.

Polynomial formulations and renormalizability in quantum gravity

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.

Minimal models on Riemann surfaces

Abstract We derive the BRST complex for the Wakimoto type free field realization of sl (3) , using as a guide the analogous complex which arises in the study of the finite dimensional algebra. We show that a quantum group structure underlies the algebra of screening operators. Some remarks on the vertex operators are made.

Self-dual formulations of D = 3 gravity theories

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

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

N=1

On the free field resolutions for coset conformal field theories

supergravity coupled to superconformal matter with