Superstrings from Hamiltonian Reduction

TL;DR

This paper explores the systematic construction of superconformal symmetry algebras in string theories with N-2 supersymmetries using quantum Hamiltonian reduction of Lie superalgebras, aiming to generalize string theory frameworks.

Contribution

It introduces a method to construct superconformal algebras for strings with N-2 supersymmetries via Hamiltonian reduction of osp(N|2), advancing the systematic understanding of string symmetries.

Findings

Constructed superconformal algebras for N-2 supersymmetric strings.

Connected Hamiltonian reduction to superstring symmetry algebra.

Discussed the BRST algebra of topological strings.

Abstract

In any string theory there is a hidden, twisted superconformal symmetry algebra, part of which is made up by the BRST current and the anti-ghost. We investigate how this algebra can be systematically constructed for strings with $N\!-\!2$ supersymmetries, via quantum Hamiltonian reduction of the Lie superalgebras $osp(N|2)$. The motivation is to understand how one could systematically construct generalized string theories from superalgebras. We also briefly discuss the BRST algebra of the topological string, which is a doubly twisted $N\!=\!4$ superconformal algebra.