REAL FORMS OF NON-ABELIAN TODA THEORIES AND THEIR W-ALGEBRAS

We consider real forms of Lie algebras and embeddings of sl(2) which a re consistent with the construction of integrable models via Hamiltoni an reduction. In other words: we examine possible non-standard reality conditions for non-abelian Toda theories. We point out in particular that the usual restriction to the maximally non-compact form of the al gebra is unnecessary, and we show how relaxing this condition can lead to new real forms of the resulting W-algebras. Previous results for a belian Toda theories are recovered as special cases. The construction can be extended straightforwardly to deal with osp(1/2) embeddings in Lie superalgebras. Two examples are worked out in detail, one based on a bosonic Lie algebra, the other based on a Lie superalgebra leading to an action which realizes the N = 4 superconformal algebra.