Remodeling the A-Model

by Andrea Brini (Section de Mathematiques, Universite de Geneve)

Tuesday 9 Nov 2010, 14:00 → 15:00 Europe/Zurich

TH Theory Conference Room (CERN)

In recent years several techniques inspired by string duality have been put forward to solve the topological A-model on toric Calabi-Yau threefolds, either via large N duality with Chern-Simons theory (the topological vertex) or using mirror symmetry and matrix-model-inspired techniques (the "Remodeled-B-Model"). I will build on recent progress in the mathematical theory of open Gromov-Witten invariants to propose, in purely A-model terms, a new formalism to compute open string amplitudes on these target spaces. In this framework, localization formulae relate D-brane amplitudes to closed string amplitudes perturbed with twisted masses through an analogue of the "loop insertion operator" of matrix models; the connection of the closed model to tau functions of 1+1 integrable hierarchies allows in turn an effective computation of the amplitudes, as well as an A-model derivation of several known results from mirror symmetry (e.g. the spectral curves). This is work in progress, partly based on previous joint work with R. Cavalieri (arXiv:1007.0934).