Hamiltonian reduction of supersymmetric WZNW models on bosonic groups and superstrings

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 non-linear 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 non-linearly 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 non-critical 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 non-standard realizations.