N=2 structures on solvable Lie algebras: the c=9 classification

Abstract

Let G be a finite-dimensional Lie algebra (not necessarily semisimple). It is known that if G is self-dual (that is, if it possesses an invariant metric) then there is a canonical N=1 superconformal algebra associated to its N=1 affinization---that is, it admits an N=1 (affine) Sugawara construction. Under certain additional hypotheses, this N=1 structure admits an N=2 extension. If this is the case, G is said to possess an N=2 structure. It is also known that an N=2 structure on a self-dual Lie algebra G is equivalent to a vector space decomposition G = G_+ \oplus G_- where G_\pm are isotropic Lie subalgebras. In other words, N=2 structures on G are in one-to-one correspondence with Manin triples (G,G_+,G_-). In this paper we exploit this correspondence to obtain a classification of the c=9 N=2 structures on self-dual solvable Lie algebras. In the process we also give some simple proofs for a variety of Lie algebraic results concerning self-dual Lie algebras admitting symplectic or Kähler structures.

49 pages in 2 columns (=25 physical pages), (uufiles-gz-9)'d .dvi file (uses AMSFonts 2.1+). Revision: Added 1 reference, corrected typos, added some more material

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Cited by in corpus (4)

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• Nonreductive WZW models and their CFTs, II: N=1 and N=2 cosets
• Classification of four dimensional real Lie bialgebras of symplectic type and their Poisson-Lie groups