Kac-Moody and Virasoro Algebras in Local Quantum Physics

  • D. I. Olive
Part of the NATO ASI Series book series (NSSB, volume 141)


These notes are based on lectures given at the Erice International School in Mathematical Physics in July 1985, and treat the Sugawara construction of the Virasoro algebra in terms of a given Kac-Moody algebra, thereby complementing previous lecture notes. Deductions are made and applied to the string theory of unified particle interactions, conformally invariant two dimensional quantum field theories and the phase transitions of two dimensional lattice systems. The ‘quark model’ representation of Kac-Moody algebras is also treated. A symmetric space criterion is derived for the quantum equivalence of a chiral model with Wess-Zumino term to a free fermion theory.


Symmetric Space Vertex Operator Energy Momentum Tensor Virasoro Algebra High Weight Representation 
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Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • D. I. Olive
    • 1
  1. 1.The Blackett LaboratoryImperial CollegeLondonUK

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