Real Forms of Non-abelian Toda Theories and their W-algebras

Abstract

We consider real forms of Lie algebras and embeddings of sl(2) which are consistent with the construction of integrable models via Hamiltonian 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 algebra is unnecessary, and we show how relaxing this condition can lead to new real forms of the resulting W-algebras. Previous results for abelian 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.

11 pages, LaTex; minor errors corrected, extra references added

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Cited by in corpus (4)

• Real Hamiltonian forms of Hamiltonian systems
• Dynkin Diagrams and Integrable Models Based on Lie Superalgebras
• On the Classification of Real Forms of Non-Abelian Toda Theories and W-algebras
• Real Hamiltonian forms of affine Toda field theories: spectral aspects