Current Algebra and Extended 2D Gravity with Higher Spin Gauge Field

  • Yutaka Matsuo
Part of the NATO ASI Series book series (NSSB, volume 245)


We discuss quantum field theory of extended two dimensional gravity associated with Zamolodchikov’s W-algebra. We introduce new type of gauge symmetry whose gauge potentials are higher rank symmetric tensor fields. In the limit that those gauge potentials are infinitesimaly small, we write down the invariant action for matter fields and extended gravity. By investigating the gauge symmetry in the light cone gauge, we find that induced quantum gravity associated with this symmetry is described by simply laced affine Lie algebras. Our result is a natural generalization of the result of Polyakov’s quantum gravity.


Gauge Transformation Gauge Symmetry Energy Momentum Tensor Current Algebra Gauge Potential 
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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Yutaka Matsuo
    • 1
  1. 1.Enrico Fermi InstituteUniversity of ChicagoChicagoUSA

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