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Current Algebra on the Torus

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Abstract

We derive the N-point one-loop correlation functions for the currents of an arbitrary affine Kac-Moody algebra. The one-loop amplitudes, which are elliptic functions defined on the torus Riemann surface, are specified by group invariant tensors and certain constant tau-dependent functions. We compute the elliptic functions via a generating function, and explicitly construct the invariant tensor functions recursively in terms of Young tableaux. The lowest tensors are related to the character formula of the representation of the affine algebra. These general current algebra loop amplitudes provide a building block for open twistor string theory, among other applications.

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Authors and Affiliations

  1. Department of Physics, University of North Carolina, Chapel Hill, NC, 27599, USA

    Louise Dolan

  2. Institute for Advanced Study, Princeton, NJ, 08540, USA

    Peter Goddard

Authors
  1. Louise Dolan
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  2. Peter Goddard
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Correspondence to Louise Dolan.

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Communicated by N.A. Nekrasov

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Dolan, L., Goddard, P. Current Algebra on the Torus. Commun. Math. Phys. 285, 219–264 (2009). https://doi.org/10.1007/s00220-008-0542-1

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  • DOI: https://doi.org/10.1007/s00220-008-0542-1

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