Emergent gravity on covariant quantum spaces in the IKKT model

TL;DR

This paper explores how perturbations of fuzzy spheres within the IKKT matrix model can give rise to emergent gravity, including Einstein equations, through a covariant noncommutative geometric framework.

Contribution

It demonstrates the emergence of 4D Einstein gravity from matrix model perturbations on fuzzy spheres, incorporating higher-spin fields and a covariant noncommutative structure.

Findings

Linearized Einstein equations derived from the matrix model.

Identification of gauge and metric fluctuations among low-spin modes.

One-loop effective action contributions computed using string state formalism.

Abstract

We study perturbations of 4-dimensional fuzzy spheres as backgrounds in the IKKT or IIB matrix model. Gauge fields and metric fluctuations are identified among the excitation modes with lowest spin, supplemented by a tower of higher-spin fields. They arise from an internal structure which can be viewed as a twisted bundle over $S^4$, leading to a covariant noncommutative geometry. The linearized 4-dimensional Einstein equations are obtained from the classical matrix model action under certain conditions, modified by an IR cutoff. Some one-loop contributions to the effective action are computed using the formalism of string states.