## Topological field theory and rational curves.(English)Zbl 0776.53043

Summary: 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 nonlinear $$\sigma$$-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.

### MSC:

 53Z05 Applications of differential geometry to physics 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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### References:

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