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Matrix factorizations and mirror symmetry: the cubic curve

Ilka Brunner1,2, Manfred Herbst1, Wolfgang Lerche1 and Johannes Walcher3

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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 m2 from the LG mirror theory. In physics terms, this gives a systematic method for determining non-perturbative Yukawa couplings for intersecting brane configurations.

Keywords

Topological Strings

D-branes

 

E-print Number: hep-th/0408243

Cited: by |

Refers: to

PACS

11.25.Uv D branes

02.40.-k Geometry, differential geometry, and topology

02.10.Yn Matrix theory

MSC

81T30 String and superstring theories; other extended objects (e.g., branes) (See also 83E30)

15A23 Factorization of matrices

15A24 Matrix equations and identities

14J32 Calabi-Yau manifolds, mirror symmetry

Subjects

Mathematical physics

Particle physics and field theory

Dates

Issue 11 (November 2006)

Received 3 October 2006, accepted for publication 5 October 2006

Published 6 November 2006



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