Off-Shell Hodge Dualities in Linearised Gravity and E11

TL;DR

This paper explores off-shell dualities in linearised gravity, revealing an infinite web of equivalent formulations involving mixed-symmetry fields linked to the E11 algebra, advancing understanding of gravitational dualities.

Contribution

It explicitly constructs off-shell dualities between dual gravitons and double-dual gravitons and demonstrates an infinite hierarchy of such dualities within the E11 framework.

Findings

Explicit off-shell dualisation between dual and double-dual gravitons.

Infinite sequence of off-shell dualities in linearised gravity.

Involvement of mixed-symmetry fields from E11 algebra.

Abstract

In a spacetime of dimension n, the dual graviton is characterised by a Young diagram with two columns, the first of length n-3 and the second of length one. In this paper we perform the off-shell dualisation relating the dual graviton to the double-dual graviton, displaying the precise off-shell field content and gauge invariances. We then show that one can further perform infinitely many off-shell dualities, reformulating linearised gravity in an infinite number of equivalent actions. The actions require supplementary mixed-symmetry fields which are contained within the generalised Kac-Moody algebra E11 and are associated with null and imaginary roots.