Worldsheet Instantons and Torsion Curves

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We study aspects of worldsheet instantons relevant to a heterotic standard model. The non-simply connected Calabi-Yau threefold used admits Z₃ x Z₃ Wilson lines, and a more detailed investigation shows that the homology classes of curves are H₂(X,Z)=Z³+Z₃+Z₃. We compute the genus-0 prepotential, this is the first explicit calculation of the Gromov-Witten invariants of homology classes with torsion (finite subgroups). In particular, some curve classes contain only a single instanton. This ensures that the Beasley-Witten cancellation of instanton contributions cannot happen on this (non-toric) Calabi-Yau threefold.