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String vertices, overlap equations, τ functions and the Hirota equation

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Abstract

String vertices,V, are shown to satisfy a new type of overlap equation of the form\(V \exp \{ ip \cdot Q^i (\xi ^i )\} = V \exp \{ ip \cdot Q^i (\xi ^i )\} \left( {\frac{{d\xi ^j }}{{d\xi ^i }}} \right)^{p^2 /2} \) as well as corresponding equations forA n andB n cycles. A special case of such an equation, when integrated, is shown to be the Hirota equation for the K−P hierarchy.

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Authors and Affiliations

  1. Institute of Theoretical Physics, Chalmers University of Technology, S-41296, Goteborg, Sweden

    B. E. W. Nilsson

  2. Mathematics Department, King's College London, Strand, WC2R 2LS, London

    P. West

Authors
  1. B. E. W. Nilsson
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  2. P. West
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Communicated by K. Gawedzki

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Nilsson, B.E.W., West, P. String vertices, overlap equations, τ functions and the Hirota equation. Commun.Math. Phys. 145, 329–344 (1992). https://doi.org/10.1007/BF02099140

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  • DOI: https://doi.org/10.1007/BF02099140

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