Extended Riemannian Geometry II: Local Heterotic Double Field Theory

Abstract

We continue our exploration of local Double Field Theory (DFT) in terms of symplectic graded manifolds carrying compatible derivations and study the case of heterotic DFT. We start by developing in detail the differential graded manifold that captures heterotic Generalized Geometry which leads to new observations on the generalized metric and its twists. We then give a symplectic pre-NQ-manifold that captures the symmetries and the geometry of local heterotic DFT. We derive a weakened form of the section condition, which arises algebraically from consistency of the symmetry Lie 2-algebra and its action on extended tensors. We also give appropriate notions of twists-which are required for global formulations-and of the torsion and Riemann tensors. Finally, we show how the observed ${\alpha }^{\prime }$-corrections are interpreted naturally in our framework.

arXiv commentv2: 30 pages, few more details added, typos fixed, published version

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Cited by in corpus (12)

• Finite deformations from a heterotic superpotential: holomorphic Chern--Simons and an $L_{\infty }$ algebra
• $L_{\infty }$ algebras and Tensor Hierarchies in Exceptional Field Theory and Gauged Supergravity
• Global Double Field Theory is Higher Kaluza-Klein Theory
• The ${\alpha }^{\prime 2}$ correction from double field theory
• Deformed graded Poisson structures, Generalized Geometry and Supergravity
• Gauged sigma-models with nonclosed 3-form and twisted Jacobi structures
• Extended Riemannian Geometry III: Global Double Field Theory with Nilmanifolds
• A note on Faddeev--Popov action for doubled-yet-gauged particle and graded Poisson geometry
• Towards an extended/higher correspondence -- Generalised geometry, bundle gerbes and global Double Field Theory
• Higher curvature Bianchi identities, generalised geometry and $L_{\infty }$ algebras
• The puzzle of global Double Field Theory: open problems and the case for a Higher Kaluza-Klein perspective
• Pre-NQ Manifolds and Correspondence Spaces: the Nilmanifold Example