Matrix Factorizations And Mirror Symmetry: The Cubic Curve

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.

23 pages, 3 figures

References in corpus (2)

• N=1 Special Geometry, Mixed Hodge Variations and Toric Geometry
• On the relation between open and closed topological strings

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