Communications in Mathematical Physics

, Volume 102, Issue 2, pp 337–347 | Cite as

Superconformal current algebras and their unitary representations

  • Victor G. Kac
  • Ivan T. Todorov


A natural supersymmetric extension\((\widehat{dG})_\kappa\) is defined of the current (= affine Kac-Moody Lie) algebra\(\widehat{dG}\); it corresponds to a superconformal and chiral invariant 2-dimensional quantum field theory (QFT), and hence appears as an ingredient in superstring models. All unitary irreducible positive energy representations of\((\widehat{dG})_\kappa\) are constructed. They extend to unitary representations of the semidirect sumSκ(G) of\((\widehat{dG})_\kappa\) with the superconformal algebra of Neveu-Schwarz, for\(\kappa = \frac{1}{2}\), or of Ramond, for κ=0.


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Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Victor G. Kac
    • 1
  • Ivan T. Todorov
    • 1
  1. 1.Department of MathematicsM.I.T.CambridgeUSA

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