Chiral gravity in higher dimensions

TL;DR

This paper develops a novel chiral gravity theory in 7 and 8 dimensions, leveraging gravitational instantons and octonionic variables, resulting in theories with G_2 and Spin(7) gauge symmetries.

Contribution

It introduces a higher-dimensional chiral gravity framework using fewer variables, based on gravitational instantons and octonionic algebra, with specific gauge symmetries.

Findings

Constructed chiral gravity in 7 and 8 dimensions.

Identified gauge symmetries as G_2 and Spin(7).

Linked non-associativity of octonions to gauge invariance issues.

Abstract

We construct a chiral theory of gravity in 7 and 8 dimensions, which are equivalent to Einstein-Cartan theory using less variables. In these dimensions, we can construct such higher dimensional chiral gravity because of the existence of gravitational instanton. The octonionic-valued variables in the theory represent the deviation from the gravitational instanton, and from their non-associativity, prevents the theory to be SO(n) gauge invariant. Still the chiral gravity holds G_2 (7-D), and Spin(7) (8-D) gauge symmetry.