Non-linear parent action and dual gravity

TL;DR

This paper presents a reformulation of non-linear Einstein gravity incorporating dual gravitons and gauge fields, using topological couplings to avoid doubling degrees of freedom, and explores gauge symmetries in relation to the E11 framework.

Contribution

It introduces a novel reformulation of Einstein gravity that includes dual gravitons without increasing degrees of freedom, emphasizing topological couplings and duality relations.

Findings

Reformulation includes dual graviton and shift gauge fields.

Metric enters via topological couplings, not Einstein-Hilbert term.

First-order duality relations characterize the field equations.

Abstract

We give a reformulation of non-linear Einstein gravity, which contains the dual graviton together with the ordinary metric and a shift gauge field. The metric does not enter through a `kinetic' Einstein-Hilbert term, but via topological couplings, and so the theory does not lead to a doubling of degrees of freedom. The field equations take the form of first-order duality relations. We analyze the gauge symmetries and comment on their meaning with regard to the E11 proposal.