Tensor hierarchies and Leibniz algebras

TL;DR

This paper establishes a canonical association between tensor hierarchies and Loday algebras, formalizing their construction and revealing a differential graded Lie algebra structure consistent with supergravity models.

Contribution

It provides a formal, explicit construction linking tensor hierarchies to Loday algebras and identifies their differential graded Lie algebra structure.

Findings

Canonical association between tensor hierarchies and Loday algebras

Explicit construction of tensor hierarchies from Loday algebras

Identification of a differential graded Lie algebra structure

Abstract

Tensor hierarchies are algebraic objects that emerge in gauging procedures in supergravity models, and that present a very deep and intricate relationship with Leibniz (or Loday) algebras. In this paper, we show that one can canonically associate a tensor hierarchy to any Loday algebra. By formalizing the construction that is performed in supergravity, we build this tensor hierarchy explicitly. We show that this tensor hierarchy can be canonically equipped with a differential graded Lie algebra structure that coincides with the one that is found in supergravity theories.