Derived Brackets and Symmetries in Generalized Geometry and Double Field Theory

TL;DR

This paper demonstrates that derived brackets serve as a unifying framework for understanding infinitesimal symmetries in generalized geometry, Double Field Theory, and heterotic theories, revealing new algebraic structures.

Contribution

It proves that derived brackets underlie symmetries in Double Field Theory and heterotic theories, and introduces conditions for these brackets to generate Lie 2-algebras.

Findings

Derived brackets describe symmetries in Double Field Theory.

Unified framework for symmetries in generalized geometry.

Conditions for brackets to produce Lie 2-algebras.

Abstract

Derived brackets as introduced and studied by Kosmann-Schwarzbach and Voronov are a powerful tool for describing and understanding infinitesimal symmetry actions relevant in physics. Roytenberg and Weinstein showed that this continues to hold for the categorified symmetries arising in Hitchin's generalized geometry. After reviewing some well-established examples, we prove that derived brackets also underlie the symmetries of Double Field Theory and heterotic Double Field Theory. This leads to a common framework for large classes of symmetries, which suggests that derived bracket constructions can function as a guiding principle in the description of infinitesimal actions of symmetries in physics. As a new result, we present sufficient conditions on a bracket to give rise to a Lie 2-algebra of symmetries via antisymmetrized derived brackets.