Extended Riemannian Geometry II: Local Heterotic Double Field Theory

TL;DR

This paper advances the mathematical framework of heterotic Double Field Theory using symplectic graded manifolds, revealing new insights into its geometry, symmetries, and $ abla$-corrections.

Contribution

It develops a differential graded manifold for heterotic Generalized Geometry and introduces a symplectic pre-NQ-manifold capturing the theory's symmetries and geometry.

Findings

Derived a weakened section condition from symmetry algebra consistency.

Introduced notions of twists, torsion, and Riemann tensors for global formulations.

Interpreted $ abla$-corrections naturally within the framework.

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 $\alpha'$-corrections are interpreted naturally in our framework.