Extended N=2 Superconformal Structure of Gravity and W-Gravity Coupled to Matter

TL;DR

This paper reveals that various string theories have a twisted N=2 superconformal symmetry, linking topological gravity with matter-gravity systems and providing new insights into W-string structures and their algebraic properties.

Contribution

It demonstrates the presence of twisted N=2 superconformal symmetry in most string theories and connects topological gravity with matter coupled to gravity, also deriving W-string operators via Hamiltonian reduction.

Findings

Identification of N=2 superconformal symmetry in string theories

Construction of ground ring generators for non-critical W3-string

Connection between W-string operators and Hamiltonian reduction

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.