Curvature and Gravity Actions for Matrix Models

TL;DR

This paper demonstrates how gravitational actions, including Einstein-Hilbert, can emerge from Yang-Mills matrix models, offering a potential non-perturbative framework for gravity and insights into vacuum energy issues.

Contribution

It introduces a method to derive gravitational actions from matrix models, connecting gravity with non-commutative gauge theories and space-time brane solutions.

Findings

Gravitational actions can be obtained from matrix models.

Space-time as 4D brane solutions is consistent with induced gravity.

Potential for a non-perturbative approach to quantum gravity.

Abstract

We show how gravitational actions, in particular the Einstein-Hilbert action, can be obtained from additional terms in Yang-Mills matrix models. This is consistent with recent results on induced gravitational actions in these matrix models, realizing space-time as 4-dimensional brane solutions. It opens up the possibility for a controlled non-perturbative description of gravity through simple matrix models, with interesting perspectives for the problem of vacuum energy. The relation with UV/IR mixing and non-commutative gauge theory is discussed.