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Superconformal current algebras and their unitary representations

Abstract

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 sumS κ(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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On leave of absence from the Institute for Nuclear Research and Nuclear Energy of the Bulgarian Academy of Sciences, BG-1184 Sofia, Bulgaria

Communicated by A. Jaffe

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Kac, V.G., Todorov, I.T. Superconformal current algebras and their unitary representations. Commun.Math. Phys. 102, 337–347 (1985). https://doi.org/10.1007/BF01229384

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Keywords

  • Neural Network
  • Statistical Physic
  • Field Theory
  • Complex System
  • Quantum Field Theory