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Communications in Mathematical Physics

, Volume 136, Issue 3, pp 451–486 | Cite as

Lie algebra cohomology andN=2 SCFT based on the GKO construction

  • Shinobu Hosono
  • Akihiro Tsuchiya
Article

Abstract

We interpretN=2 superconformal field theories (SCFTs) formulated by Kazama and Suzuki via Goddard-Kent-Olive (GKO) construction from a viewpoint of the Lie algebra cohomology theory for the affine Lie algebra. We determine the cohomology group completely in terms of a certain subset of the affine Weyl group. We find that this subset describing the cohomology group can be obtained from its classical counterpart by the action of the Dynkin diagram automorphisms. Some algebra automorphisms of theN=2 superconformal algebra are also formulated. Utilizing the algebra automorphisms, we study the field identification problem for the branching coefficient modules in the GKO-construction. Also the structure of the Poincaré polynomial defined for eachN=2 theory is revealed.

Keywords

Neural Network Identification Problem Quantum Computing Weyl Group Cohomology Group 
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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Shinobu Hosono
    • 1
  • Akihiro Tsuchiya
    • 2
  1. 1.Department of PhysicsUniversity of TokyoTokyoJapan
  2. 2.Department of MathematicsNagoya UniversityNagoyaJapan

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