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Topological field theory and rational curves

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We analyze the quantum field theory corresponding to a string propagating on a Calabi-Yau threefold. This theory naturally leads to the consideration of Witten's topological non-linear σ-model and the structure of rational curves on the Calabi-Yau manifold. We study in detail the case of the world-sheet of the string being mapped to a multiple cover of an isolated rational curve and we show that a natural compactification of the moduli space of such a multiple cover leads to a formula in agreement with a conjecture by Candelas, de la Ossa, Green and Parkes.

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Authors and Affiliations

  1. Department of Theoretical Physics, University of Oxford, 1 Keble Road, OX1 3NP, Oxford, UK

    Paul S. Aspinwall

  2. Department of Mathematics, Duke University, 27706, Durham, NC, USA

    David R. Morrison

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  1. Paul S. Aspinwall
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  2. David R. Morrison
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Communicated by S.-T. Yau

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Aspinwall, P.S., Morrison, D.R. Topological field theory and rational curves. Commun.Math. Phys. 151, 245–262 (1993). https://doi.org/10.1007/BF02096768

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