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Functional determinants on Mandelstam diagrams

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Abstract

We investigate the special properties of Mandelstam metrics in regard to changing weights in path integrals and relations between determinants of different spins. Regularizations of determinants are discussed along the lines of Sonoda. Weyl anomalies developing at zeroes of metrics in reparametrization invariant regularizations are evaluated in terms of Arakelov metrics. Holomorphic forms are constructed, and determinant identities for Arakelov and Mandelstam metrics rigorously established for any weight and generic even and odd spin structures.

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Authors and Affiliations

  1. Department of Physics, University of California, 90024, Los Angeles, CA, USA

    Eric D'Hoker

  2. Department of Mathematics, Columbia University, 10027, New York, NY, USA

    D. H. Phong

Authors
  1. Eric D'Hoker
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  2. D. H. Phong
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Communicated by S.-T. Yau

Work supported by the National Science Foundation under grants PHY-80-19754 PHY-86-13201 and DMS-87-04209

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D'Hoker, E., Phong, D.H. Functional determinants on Mandelstam diagrams. Commun.Math. Phys. 124, 629–645 (1989). https://doi.org/10.1007/BF01218453

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  • DOI: https://doi.org/10.1007/BF01218453

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