2008/03/25 by Evgeny Feigin
Mathematics · #Algebraic Geometry and Number Theory #Combinatorics #Genus #Geometric and Algebraic Topology #Geometry #Homogeneous space #Homotopy and Cohomology in Algebraic Topology #Mathematical physics #Mathematics #Modulo #Pure mathematics #String theory #Symplectic geometry #math.AG #math.QA #msc:17B65 #msc:32G15
paper · pdf · doi:10.1016/j.geomphys.2009.04.014
published as J.Geom.Phys.59:1127-1136,2009 · 15 pages
arxiv created 2008/03/25 · openalex publication_date 2009/05/10 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In [Gi3] Givental introduced and studied a space of formal genus zero Gromov-Witten theories GW0, i.e. functions satisfying string and dilaton equations and topological recursion relations. A central role in the theory plays the geometry of certain Lagrangian cones and a twisted symplectic group of hidden symmetries. In this note we show that the Lagrangian cones description of the action of this group coincides with the genus zero part of Givental's quantum Hamiltonian formalism. As an application we identify explicitly the space of N=1 formal genus zero GW theories with lower-triangular twisted symplectic group modulo the string flow.