2011/02/28 by Andrea Brini · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #Combinatorics #Instanton #Integrable system #Mathematical physics #Mathematics #Moduli #Moduli space #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum mechanics #Relationship between string theory and quantum field theory #Theoretical physics #Topological string theory #Topology (electrical circuits) #hep-th #math-ph #math.AG #math.MP
paper · pdf · doi:10.1007/s00220-012-1489-9
49 pages, 10 figures; v2: typos fixed, updated references, version to appear on Comm. Math. Phys
arxiv created 2012/05/04 · openalex publication_date 2012/05/12 · arxiv updated 2015/05/27 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
We set up, purely in A-model terms, a novel formalism for the global solution of the open and closed topological A-model on toric Calabi-Yau threefolds. The starting point is to build on recent progress in the mathematical theory of open Gromov-Witten invariants of orbifolds; we interpret the localization formulae as relating D-brane amplitudes to closed string amplitudes perturbed with twisted masses through an analogue of the "loop insertion operator" of matrix models. We first generalize this form of open/closed string duality to general toric backgrounds in all chambers of the stringy Kaehler moduli space; secondly, we display a neat connection of the (gauged) closed string side to tau functions of 1+1 Hamiltonian integrable hierarchies, and exploit it to provide an effective computation of open string amplitudes. In doing so, we also provide a systematic treatment of the change of flat open moduli induced by a phase transition in the closed moduli space. We test our proposal in detail by providing an extensive number of checks. We also use our formalism to give a localization-based derivation of the Hori-Vafa spectral curves as coming from a resummation of A-model disc instantons.