2-vector bundles, D-branes and Frobenius Manifolds

2015/07/30 by Anibal Amoreo, Amoreo, Anibal, Jorge A. Devoto +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #math.AG #math.AT #math.CT

paper · pdf · doi:10.48550/arxiv.1507.08485

arxiv created 2015/07/30 · arxiv updated 2015/07/31

Abstract

We show that if M is a Frobenius manifold of dimension n such that T_x M is semisimple for every x ∈ M, then there exists a canonical 2-vector bundle B over M of rank n. This 2-vector bundle encodes the information about the maximal category of D-branes associated to the open closed topological field theories defined by the Frobenius algebras T_x M. In particular this construction answers a conjecture of Graeme Segal in~\citesegal07:_what_is_ellip_objec. We also explain the relation of the labels of the D-branes to Azumaya algebras and twisted vector bundles on the spectral cover S of M.

Related

• On 2-dimensional topological field theories
• Frobenius Manifolds, Spectral Curves, and Integrable Hierarchies
• Topological Frobenius algebras
• 2-vector bundles
• The action of the Frobenius map on rank 2 vector bundles over a supersingular genus 2 curve in characteristic 2