Open string instantons and relative stable morphisms

Details Open string instantons and relative stable morphisms Open string instantons and relative stable morphisms

2001-03-13

arxiv.org/abs/hep-th/0103100v4

Adv.Theor.Math.Phys.5:67-91,2002

Physics

High Energy Physics

High Energy Physics - Theory

This is the version published by Geometry & Topology Monographs on 22 April 2006

Scientific paper

10.2140/gtm.2006.8.49

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.

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