Worldsheet Instantons and Torsion Curves, Part B: Mirror Symmetry

Details Worldsheet Instantons and Torsion Curves, Part B: Mirror Symmetry Worldsheet Instantons and Torsion Curves, Part B: Mirror Symmetry

2007-04-03

arxiv.org/abs/0704.0449v1

JHEP0710:023,2007

Physics

High Energy Physics

High Energy Physics - Theory

59 pages, LaTeX

Scientific paper

10.1088/1126-6708/2007/10/023

We apply mirror symmetry to the problem of counting holomorphic rational curves in a Calabi-Yau threefold X with Z_3 x Z_3 Wilson lines. As we found in Part A [hep-th/0703182], the integral homology group H_2(X,Z)=Z^3 + Z_3 + Z_3 contains torsion curves. Using the B-model on the mirror of X as well as its covering spaces, we compute the instanton numbers. We observe that X is self-mirror even at the quantum level. Using the self-mirror property, we derive the complete prepotential on X, going beyond the results of Part A. In particular, this yields the first example where the instanton number depends on the torsion part of its homology class. Another consequence is that the threefold X provides a non-toric example for the conjectured exchange of torsion subgroups in mirror manifolds.

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