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String quantization on group manifolds and the holomorphic geometry of DiffS 1/S 1

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Abstract

The recent results by Bowick and Rajeev on the relation of the geometry of DiffS 1/S 1 and string quantization in ℝd are extended to a string moving on a group manifold. A new derivation of the curvature formula (−26/12m 3+1/6m)δ n, −m for the canonical holomorphic line bundle over DiffS 1/S 1 is given which clarifies the relation of that bundle with the complex line bundles over infinite-dimensional Grassmannians, studied by Pressley and Segal.

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Author notes

  1. Jouko Mickelsson

    Present address: Department of Mathematics, University of Jyväskylä, Seminaarinkatu 15, SF-40100, Jyväskylä 10, Finland

Authors and Affiliations

  1. Center for Theoretical Physics, Laboratory for Nuclear Science, and Department of Physics, Massachusetts Institute of Technology, 02139, Cambridge, MA, USA

    Jouko Mickelsson

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  1. Jouko Mickelsson
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Additional information

Communicated by A. Jaffe

This work is supported in part by funds provided by the U.S. Department of Energy (D.O.E.) under contract #DE-AC02-76ER03069

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Mickelsson, J. String quantization on group manifolds and the holomorphic geometry of DiffS 1/S 1 . Commun.Math. Phys. 112, 653–661 (1987). https://doi.org/10.1007/BF01225379

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  • DOI: https://doi.org/10.1007/BF01225379

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