1998/02/28 by J. M. Evans, J.M. Evans, J. O. Madsen +1 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Conformal map #Embedding #Homotopy and Cohomology in Algebraic Topology #Lie algebra #Lie group #Real form #Simple (philosophy) #Toda lattice #hep-th
paper · pdf · doi:10.1016/s0550-3213(98)00693-2
published in Nuclear Physics B 536(3), 657-703 (Elsevier BV) · 42 pages, LaTeX; Minor corrections to ensure consistent conventions; some references added
openalex publication_date 1998/12/01 · arxiv created 1999/02/26 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.