Communications in Mathematical Physics

, Volume 181, Issue 3, pp 529–568 | Cite as

Drinfeld-Sokolov gravity

  • Roberto Zucchini


A lagrangian euclidean model of Drinfeld-Sokolov (DS) reduction leading to generalW-algebras on a Riemann surface of any genus is presented. The background geometry is given by the DS principal bundleK associated to a complex Lie groupG and anSL(2,ℂ) subgroupS. The basic fields are a hermitian fiber metricH ofK and a (0, 1) Koszul gauge fieldA* ofK valued in a certain negative graded subalgebrar ofg related tos. The action governing theH andA* dynamics is the effective action of a DS field theory in the geometric background specified byH andA*. Quantization ofH andA* implements on one hand the DS reduction and on the other defines a novel model of 2d gravity, DS gravity. The gauge fixing of the DS gauge symmetry yields an integration on a moduli space of DS gauge equivalence classes ofA* configurations, the DS moduli space. The model has a residual gauge symmetry associated to the DS gauge transformations leaving a given fieldA* invariant. This is the DS counterpart of conformal symmetry. Conformal invariance and certain non-perturbative features of the model are discussed in detail.


Modulus Space Riemann Surface Gauge Transformation Gauge Symmetry Gauge fieldA 


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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Roberto Zucchini
    • 1
  1. 1.Dipartimento di FisicaUniversità degli Studi di BolognaBolognaItaly

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