Classical Hamiltonian Reduction and Superconformal Algebras

TL;DR

This paper explores how Hamiltonian reduction techniques relate to superconformal algebras, using free-field representations and gauge transformations to connect different symmetry structures in two-dimensional theories.

Contribution

It clarifies the connection between Polyakov's soldering procedure and Hamiltonian reduction, extending the formalism to N=1 and N=2 superconformal algebras using superfield representations.

Findings

Polyakov's method relates to Hamiltonian reduction transparently.

Superdiffeomorphisms derived from super gauge transformations.

Phase space of supercurrent algebra connects to superconformal algebra.

Abstract

The Polyakov's "soldering procedure" which shows how two-dimensional diffeomorphisms can be obtained from SL(2,R) gauge transformations is discussed using the free-field representation of SL(2,R) current algebra. Using this formalism, the relation of Polyakov's method to that of the Hamiltonian reduction becomes transparent. This discussion is then generalised to N=1 superdiffeomorphisms which can be obtained from N=1 super Osp(1,2) gauge transformations. It is also demonstrated that the phase space of the Osp(2,2) supercurrent algebra represented by free superfields is connected to the classical phase space of N=2 superconformal algebra via Hamiltonian reduction.}