2001/03/31 by Sheldon Katz, Chiu-Chu Melissa Liu · 1 citation
Mathematics · Physics and Astronomy · #hep-th #math.AG #math.SG #msc:14N35 #msc:32G81 #msc:53D45
paper · pdf · doi:10.2140/gtm.2006.8.1
published as Adv.Theor.Math.Phys. 5 (2002) 1-49 and Geom. Topol. Monogr. 8 (2006) 1-47 · This is the version published by Geometry & Topology Monographs on 22 April 2006
arxiv created 2009/03/13 · arxiv updated 2009/11/30
In this paper, we present foundational material towards the development of a rigorous enumerative theory of stable maps with Lagrangian boundary conditions, ie stable maps from bordered Riemann surfaces to a symplectic manifold, such that the boundary maps to a Lagrangian submanifold. Our main application is to a situation where our proposed theory leads to a well-defined algebro-geometric computation very similar to well-known localization techniques in Gromov-Witten theory. In particular, our computation of the invariants for multiple covers of a generic disc bounding a special Lagrangian submanifold in a Calabi-Yau threefold agrees completely with the original predictions of Ooguri and Vafa based on string duality. Our proposed invariants depend more generally on a discrete parameter which came to light in the work of Aganagic, Klemm, and Vafa which was also based on duality, and our more general calculations agree with theirs up to sign.