Symplectic structures on the integration of exact Courant algebroids

Abstract

We construct an infinite-dimensional symplectic 2-groupoid as the integration of an exact Courant algebroid. We show that every integrable Dirac structure integrates to a "Lagrangian" sub-2-groupoid of this symplectic 2-groupoid. As a corollary, we recover a result of Bursztyn-Crainic-Weinstein-Zhu that every integrable Dirac structure integrates to a presymplectic groupoid.

18 pages

References in corpus (5)

• AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories
• From double Lie groupoids to local Lie 2-groupoids
• Integration of Exact Courant Algebroids
• Constant Symplectic 2-groupoids
• Poisson manifolds and their associated stacks

Cited by in corpus (5)

• Global Aspects of Doubled Geometry and Pre-rackoid
• Momentum section on Courant algebroid and constrained Hamiltonian mechanics
• The geometry of graded cotangent bundles
• Constant Symplectic 2-groupoids
• Differentiating $L_{\infty }$ groupoids