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

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

1996-05-17

arxiv.org/abs/hep-th/9605126v2

Phys.Lett. B384 (1996) 131-139

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1016/0370-2693(96)00788-5

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.

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