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.

48 pages

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• On Minimal N=4 Topological Strings And The (1,k) Minimal Bosonic String
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• New Spinor Field Realizations of the Non-Critical $W_3$ String
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• On the Lagrangian Realization of Non-Critical $\mathcal{W}$-Strings
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