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Matrix Factorizations And Mirror Symmetry: The Cubic Curve

Ilka Brunner·Manfred Herbst·Wolfgang Lerche·Johannes Walcher
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Abstract

We revisit open string mirror symmetry for the elliptic curve, using matrix factorizations for describing D-branes on the B-model side. We show how flat coordinates can be intrinsically defined in the Landau-Ginzburg model, and derive the A-model partition function counting disk instantons that stretch between three D-branes. In mathematical terms, this amounts to computing the simplest Fukaya product m_2 from the LG mirror theory. In physics terms, this gives a systematic method for determining non-perturbative Yukawa couplings for intersecting brane configurations.

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Ilka Brunner, Manfred Herbst, Wolfgang Lerche, Johannes Walcher. 2004-08-31. Matrix Factorizations And Mirror Symmetry: The Cubic Curve. https://doi.org/10.1088/1126-6708%2F2006%2F11%2F006

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