Hamiltonian Reduction and Topological Conformal Algebra in $c\leq 1$ Non-critical Strings

TL;DR

This paper explores the Hamiltonian reduction of affine Lie superalgebra $sl(2|1)^{(1)}$, deriving free field realizations of topological algebras relevant to $c\,\leq\,1$ non-critical string theories, both classically and quantum mechanically.

Contribution

It provides a new free field realization of the topological algebra in $c\leq1$ non-critical strings through Hamiltonian reduction and BRST cohomology analysis.

Findings

Derived classical free field realization of the topological algebra.

Obtained quantum free field expression via BRST cohomology.

Connected algebraic structures to non-critical string models.

Abstract

We study the hamiltonian reduction of affine Lie superalgebra $sl(2|1)^{(1)}$. Based on a scalar Lax operator formalism, we derive the free field realization of the classical topological topological algebra which appears in the $c\leq1$ non-critical strings. In the quantum case, we analyze the BRST cohomology to get the quantum free field expression of the algebra.