Classical space-time geometry in the IKKT matrix model

TL;DR

This paper explores how classical 3+1-dimensional space-time geometries can emerge from the IKKT matrix model using covariant quantum spaces, providing a practical method and analyzing the impact of higher-spin contributions.

Contribution

It offers an explicit recipe for reconstructing generic classical geometries within the IKKT matrix model, including the role of fuzzy extra dimensions and higher-spin effects.

Findings

Higher-spin contributions do not significantly alter the physical content in the weak gravity regime.

The framework supports emergent gravity with an induced Einstein-Hilbert action.

Explicit construction methods for classical geometries are provided.

Abstract

We discuss the reconstruction of generic 3+1-dimensional space-time geometries from covariant quantum spaces as backgrounds in the IKKT matrix model. An explicit recipe to realize generic classical geometries is provided. Even though this typically entails some higher-spin contributions, these do not significantly modify the physical content of the model in the weak gravity regime. This justifies the framework for emergent gravity given by the semi-classical matrix model, supplemented by an induced Einstein-Hilbert action which arises in the presence of fuzzy extra dimensions.