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Communications in Mathematical Physics

, Volume 118, Issue 4, pp 651–701 | Cite as

Determinant bundles and Virasoro algebras

  • A. A. Beilinson
  • V. V. Schechtman
Article

Abstract

We consider the interplay of infinite-dimensional Lie algebras of Virasoro type and moduli spaces of curves, suggested by string theory. We will see that the infinitesimal geometry of determinant bundles is governed by Virasoro symmetries. The Mumford forms are just invariants of these symmetries. The representations of Virasoro algebra define (twisted)D-modules on moduli spaces; theseD-modules are equations on correlators in conformal field theory.

Keywords

Neural Network Statistical Physic Field Theory Complex System String Theory 
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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • A. A. Beilinson
    • 1
  • V. V. Schechtman
    • 2
  1. 1.MoscowUSSR
  2. 2.Institute of Problems of Microelectronics Technology and Superpure MaterialsChernogolovka, Moscow districtUSSR

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