Algebroids, AKSZ Constructions and Doubled Geometry

Vincenzo Emilio Marotta, Richard J. Szabo

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Abstract

We give a self-contained survey of some approaches aimed at a global description of the geometry underlying double field theory. After reviewing the geometry of Courant algebroids and their incarnations in the AKSZ construction, we develop the theory of metric algebroids including their graded geometry. We use metric algebroids to give a global description of doubled geometry, incorporating the section constraint, as well as an AKSZ-Type construction of topological doubled sigma-models. When these notions are combined with ingredients of para-Hermitian geometry, we demonstrate how they reproduce kinematical features of double field theory from a global perspective, including solutions of the section constraint for Riemannian foliated doubled manifolds, as well as a natural notion of generalized T-duality for polarized doubled manifolds. We describe the L∞-Algebras of symmetries of a doubled geometry, and briefly discuss other proposals for global doubled geometry in the literature.

Original languageEnglish
Pages (from-to)354-402
Number of pages49
JournalComplex Manifolds
Volume8
Issue number1
DOIs
Publication statusPublished - 2021

Keywords

  • Algebroids
  • Doubled geometry
  • Para-Hermitian geometry
  • Sigma-models
  • String theory
  • T-duality

ASJC Scopus subject areas

  • Geometry and Topology

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