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