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Open string instantons and relative stable morphisms

Jun Li and Yun S Song

Geometry & Topology Monographs 8 (2006) 49–72

DOI: 10.2140/gtm.2006.8.49

arXiv: hep-th/0103100


We show how topological open string theory amplitudes can be computed by using relative stable morphisms in the algebraic category. We achieve our goal by explicitly working through an example which has been previously considered by Ooguri and Vafa from the point of view of physics. By using the method of virtual localization, we successfully reproduce their results for multiple covers of a holomorphic disc, whose boundary lies in a Lagrangian submanifold of a Calabi–Yau 3–fold, by Riemann surfaces with arbitrary genera and number of boundary components. In particular we show that in the case we consider there are no open string instantons with more than one boundary component ending on the Lagrangian submanifold.

Reproduced by kind permission of International Press from: Advances in Theoretical and Mathematical Physics 5 (2002) 69–91


open string theory, Gromov-Witten invariants, large N duality

Mathematical Subject Classification

Primary: 14N35

Secondary: 14D21


Received: 26 April 2001
Published: 22 April 2006

Jun Li
Department of Mathematics
Stanford University
California 94305
Yun S Song
Department of Physics, and SLAC
Stanford University
California 94305