Topological Strings from WZW Models

TL;DR

This paper demonstrates that topological string theories can be derived from WZW models via hamiltonian reduction, revealing a deep algebraic structure linking superconformal algebras and string models.

Contribution

It shows how the BRST structure of topological strings is encoded in the small N=4 superconformal algebra and derives topological strings from WZW models through hamiltonian reduction.

Findings

Topological strings can be obtained from WZW models.

The BRST structure is encoded in the small N=4 superconformal algebra.

Embedding of bosonic string into topological string is demonstrated.

Abstract

We show that the BRST structure of the topological string is encoded in the ``small'' $N=4$ superconformal algebra, enabling us to obtain, in a non-trivial way, the string theory from hamiltonian reduction of $A(1|1)$. This leads to the important conclusion that not only ordinary string theories, but topological strings as well, can be obtained, or even defined, by hamiltonian reduction from WZW models. Using two different gradations, we find either the standard $N=2$ minimal models coupled to topological gravity, or an embedding of the bosonic string into the topological string. We also comment briefly on the generalization to super Lie algebras $A(n|n)$.