Emergent Geometry and Gravity from Matrix Models: an Introduction

TL;DR

This paper reviews how space-time and gravity can emerge from matrix models, describing noncommutative geometries and their implications for quantum gravity, with a focus on the IKKT model and its solutions.

Contribution

It introduces a framework for emergent gravity from matrix models, detailing the effective geometry, types of solutions, and their potential for quantum gravity.

Findings

Identification of harmonic and Einstein geometries in matrix models

Analysis of the role of vacuum energy in the harmonic branch

Discussion of the IKKT model as a candidate for quantum gravity

Abstract

A introductory review to emergent noncommutative gravity within Yang-Mills Matrix models is presented. Space-time is described as a noncommutative brane solution of the matrix model, i.e. as submanifold of \R^D. Fields and matter on the brane arise as fluctuations of the bosonic resp. fermionic matrices around such a background, and couple to an effective metric interpreted in terms of gravity. Suitable tools are provided for the description of the effective geometry in the semi-classical limit. The relation to noncommutative gauge theory and the role of UV/IR mixing is explained. Several types of geometries are identified, in particular "harmonic" and "Einstein" type of solutions. The physics of the harmonic branch is discussed in some detail, emphasizing the non-standard role of vacuum energy. This may provide new approach to some of the big puzzles in this context. The IKKT model with D=10 and close relatives are singled out as promising candidates for a quantum theory of fundamental interactions including gravity.