Symmetries and Compactifications of (4,0) Conformal Gravity

TL;DR

This paper investigates the properties of a 6-dimensional (4,0) superconformal gravity theory, its dimensional reduction to 4D, and the duality symmetries that emerge, with implications for non-geometric gravity frameworks.

Contribution

It analyzes the toroidal reduction of (4,0) conformal gravity and reveals an $SL(2, ext{Z})$ duality symmetry affecting the linearized gravity sector.

Findings

Discovery of $SL(2, ext{Z})$ duality symmetry in 4D reduction

Interchange of Einstein equations and Bianchi identities under duality

Discussion of potential extension to interacting theories and non-geometric gravity

Abstract

The free (4,0) superconformal theory in 6 dimensions and its toroidal dimensional reductions are studied. The reduction to four dimensions on a 2-torus has an $SL(2,\Z)$ duality symmetry that acts non-trivially on the linearised gravity sector, interchanging the linearised Einstein equations and Bianchi identities and giving a self-duality between strong and weak coupling regimes. The possibility of this extending to an interacting form of the theory is discussed and implications for the non-geometric picture of gravity that could emerge are considered.