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Anomalies and curvature ofW manifolds

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Abstract

We study the holomorphic structure of certain complex manifolds associated withW ∞ algebras, namely, the flag manifoldsW ∞/T ∞ andW 1+∞/T 1+∞, and the spacesW ∞/SL(∞),R) andW 1+∞/GL(∞,R), whereT ∞ andT 1+∞ are the maximal tori inW ∞ andW 1+∞. We compute their Ricci curvature and show how the results are related to the anomaly-freedom conditions forW ∞ andW 1+∞. We discuss the relation of these manifolds with extensions of universal Teichmüller space.

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Authors and Affiliations

  1. Center for Theoretical Physics, Texas A&M University, 77843-4242, College Station, TX, USA

    C. N. Pope & X. Shen

  2. Department of Physics, University of Southern California, 90089-0484, Los Angeles, CA, USA

    L. J. Romans & E. Sezgin

Authors
  1. C. N. Pope
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  2. L. J. Romans
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  3. E. Sezgin
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  4. X. Shen
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Additional information

Communicated by N. Yu. Reshetikhin

Supported in part by the U.S. Department of Energy, under grant DE-AS05-81ER40039

Supported in part by the U.S. Department of Energy, under grant DE-FG03-84ER40168

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Pope, C.N., Romans, L.J., Sezgin, E. et al. Anomalies and curvature ofW manifolds. Commun.Math. Phys. 140, 149–157 (1991). https://doi.org/10.1007/BF02099295

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  • DOI: https://doi.org/10.1007/BF02099295

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