Extended N = 2 superconformal structure of gravity and W-gravity coupled to matter

Abstract

We show that almost all string theories, including the bosonic string, the superstring and W-string theories, possess a twisted N = 2 superconformal symmetry. This enables us to establish a connection between topological gravity and the field theoretical description of matter coupled to gravity. We also show how the BRST operators of the W n -string can be obtained by hamiltonian reduction of SL( n|; n−1). The tachyonic and ground ring states of W-strings are described in the light of the N = 2 superconformal structure, and the ground ring generators for the non-critical W 3-string are explicitly constructed. The relationship to G/G models and quantum integrable systems is also briefly described.