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 \brs 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.