Hamiltonian Reduction of Supersymmetric WZNW Models on Bosonic Groups and Superstrings

TL;DR

The paper derives a supersymmetric super-Toda model from a constrained supersymmetric WZNW theory on $sl(2,R)$, revealing a new superstring-related equation with nonlinear supersymmetry and spontaneous breaking.

Contribution

It introduces a novel Hamiltonian reduction method producing super-Toda models and super-W algebras from bosonic Lie algebras, connecting to superstring theories.

Findings

Derived a super-Toda model from supersymmetric WZNW theory.

Identified a superconformal system similar to noncritical fermionic strings.

Generalized the reduction to produce super-W algebras from any bosonic Lie algebra.

Abstract

It is shown that an alternative supersymmetric version of the Liouville equation extracted from D=3 Green-Schwarz superstring equations naturally arises as a super-Toda model obtained from a properly constrained supersymmetric WZNW theory based on the $sl(2, R)$ algebra. Hamiltonian reduction is performed by imposing a nonlinear superfield constraint which turns out to be a mixture of a first- and second-class constraint on supercurrent components. Supersymmetry of the model is realized nonlinearly and is spontaneously broken. The set of independent current fields which survive the Hamiltonian reduction contains (in the holomorphic sector) one bosonic current of spin 2 (the stress--tensor of the spin 0 Liouville mode) and two fermionic fields of spin ${3/2}$ and $-1/2$. The $n=1$ superconformal system thus obtained is of the same kind as one describing noncritical fermionic strings in a universal string theory. The generalization of this procedure allows one to produce from any bosonic Lie algebra super--Toda models and associated super-W algebras together with their nonstandard realizations.