Exploring the gravity sector of emergent higher-spin gravity: effective action and a solution

TL;DR

This paper investigates the semi-classical gravity sector within Yang-Mills matrix models on a quantum FLRW background, deriving an effective action and presenting an explicit solution describing a gravitational field coupled to a dilaton.

Contribution

It introduces a covariant geometric framework for emergent higher-spin gravity, deriving an effective action that includes Einstein-Hilbert, dilaton, axion, and Maxwell terms, and provides an explicit solution.

Findings

Derived an effective action reproducing equations of motion.

Found an explicit rotationally invariant gravitational solution.

Connected the geometric structure to a frame from Poisson brackets.

Abstract

We elaborate the description of the semi-classical gravity sector of Yang-Mills matrix models on a covariant quantum FLRW background. The basic geometric structure is a frame, which arises from the Poisson structure on an underlying $S^2$ bundle over space-time. The equations of motion for the associated Weitzenb\"ock torsion obtained in arXiv:2002.02742 are rewritten in the form of Yang-Mills-type equations for the frame. An effective action is found which reproduces these equations of motion, which contains an Einstein-Hilbert term coupled to a dilaton, an axion and a Maxwell-type term for the dynamical frame. An explicit rotationally invariant solution is found, which describes a gravitational field coupled to the dilaton.