Current Algebra and Extended 2D Gravity with Higher Spin Gauge Field
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.
KeywordsGauge Transformation Gauge Symmetry Energy Momentum Tensor Current Algebra Gauge Potential
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- Bilal, A. and Gervais, J.-L., preprint LPTENS 88/36 (1988).Google Scholar
- Zamolodchikov, A.B., Theor.Math.Phys. 99 (1985) 108;Google Scholar
- [6c]Lukyanov, S.L. and Fateev, V.A., Kiev preprints ITP-88–74P, 75P, 6P;Google Scholar
- Bershadsky, M. and Ooguri, H., Princeton preprint IASSN-HEP-89/09 (1989);Google Scholar
- [7a]Alekseev, A. and Shatashivili, S., Nuclear Physics (1989);Google Scholar
- [7b]Polyakov, A.M., MIT preprint (1989).Google Scholar
- Polyakov, A.M., “Gauge Field and Strings” (1988)Google Scholar
- Park, H., preprint (1989).Google Scholar
- Kac, V. and Wakimoto, M., Proc.Natl.Acad.Sci.USA 85 Google Scholar