On the Classification of Real Forms of Non-Abelian Toda Theories and W-algebras

Details On the Classification of Real Forms of Non-Abelian Toda Theories and W-algebras On the Classification of Real Forms of Non-Abelian Toda Theories and W-algebras

1998-02-27

arxiv.org/abs/hep-th/9802201v2

Nucl.Phys. B536 (1998) 657-703; Erratum-ibid. B547 (1999) 665-666

Physics

High Energy Physics

High Energy Physics - Theory

42 pages, LaTeX; Minor corrections to ensure consistent conventions; some references added

Scientific paper

10.1016/S0550-3213(98)00693-2

We consider conformal non-Abelian Toda theories obtained by hamiltonian reduction from Wess-Zumino-Witten models based on general real Lie groups. We study in detail the possible choices of reality conditions which can be imposed on the WZW or Toda fields and prove correspondences with sl(2,R) embeddings into real Lie algebras and with the possible real forms of the associated W-algebras. We devise a a method for finding all real embeddings which can be obtained from a given embedding of sl(2,C) into a complex Lie algebra. We then apply this to give a complete classification of real embeddings which are principal in some simple regular subalgebra of a classical Lie algebra.

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