Elsevier

Nuclear Physics B

Volume 473, Issue 3, 12 August 1996, Pages 616-630
Nuclear Physics B

Applications of the Dotsenko-Fateev integral in random-matrix models

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Abstract

The characteristic multi-dimensional integrals that represent physical quantities in random-matrix models, when calculated within the supersymmetry method, can be related to a class of integrals introduced in the context of two-dimensional conformal field theories by Dotsenko and Fateev. Known results on these Dotsenko-Fateev integrals provide a means by which to perform explicit calculations (otherwise difficult) in random-matrix theory. We illustrate this by (i) an evaluation of the mean squared S-matrix elements for the Gaussian orthogonal ensemble coupled with M external channels, and (ii) a direct derivation of the asymptotic behaviour of the dynamical density-density cotrelator in the limit of large spatial and temporal separation for the Calogero-Sutherland model which, at certain couplings, is known to map onto the parameter-dependent random-matrix ensembles.

References (15)

  • J.J.M. Verbaarschot et al.

    Phys. Rep.

    (1985)
  • S. Iida et al.

    Ann. Phys.

    (1990)
  • Z. Pluhař et al.

    Ann. Phys.

    (1995)
  • V.S. Dotsenko et al.

    Nucl. Phys. B

    (1985)
  • P.J. Forrester

    Nucl. Phys. B

    (1992)
  • Z.N.C. Ha

    Nucl. Phys. B

    (1995)
  • M.L. Mehta

    Random matrices

    (1991)
There are more references available in the full text version of this article.

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Postal address: Aeronautical Research Laboratory, Air Operations Division, PO. Box 4331, Melbourne 3001, Australia.

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