Worldsheet Instantons and Torsion Curves

We study aspects of worldsheet instantons relevant to a heterotic standard model. The non-simply connected Calabi-Yau threefold used admits Z3 × Z3 Wilson lines, and a more detailed investigation shows that the homology classes of curves are H2(X, Z) = Z 3 ⊕(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)[1, 2, 3]. 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. 1. Heterotic Standard Models 1.1. Heterotic M-theory. Probably the most promising corner of string theory to construct models with realistic particle spectra is heterotic M-theory, also known as the Horava Witten setup [4, 5]. In it, the spacetime is taken to be Minkowski space R3,1 times a Calabi-Yau threefold X times an interval I in the eleventh direction. The two 10-dimensional boundaries each support a E8 gauge theory, one of which should be broken by instantons and/or Wilson lines to the standard model gauge group. The other Ehid 8 is then hidden and only couples gravitationally to the visible sector. In 1991 Mathematics Subject Classification. Primary 81T30, 14N35; Secondary 14D21, 53D45.