Open string instantons and relative stable morphisms
Jun Li, Yun S. Song · Advances in Theoretical and Mathematical Physics · 2001
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.