Oxidizing Borcherds symmetries

TL;DR

This paper explores the structure of Borcherds algebras related to supergravity tensor hierarchies, revealing their embeddings, unification, and duality properties across different dimensions, with novel algebraic constructions for D>8.

Contribution

It introduces a unifying Borcherds algebra framework for tensor hierarchies in supergravity and explains their dimensional embeddings and dualities.

Findings

Borcherds algebras in various dimensions are embedded into a single unifying algebra.

The algebraic structure reflects physical oxidation processes.

New Borcherds algebras for D>8 generate the same tensor hierarchy as known ones.

Abstract

The tensor hierarchy of maximal supergravity in D dimensions is known to be closely related to a Borcherds (super)algebra that is constructed from the global symmetry group E(11-D). We here explain how the Borcherds algebras in different dimensions are embedded into each other and can be constructed from a unifying Borcherds algebra. The construction also has a natural physical explanation in terms of oxidation. We then go on to show that the Hodge duality that is present in the tensor hierarchy has an algebraic counterpart. For D>8 the Borcherds algebras we find differ from the ones existing in the literature although they generate the same tensor hierarchy.