Emergent Gravity from Noncommutative Gauge Theory

TL;DR

This paper demonstrates that noncommutative gauge theories derived from matrix models naturally give rise to emergent gravity, linking gauge fields and spacetime geometry through a dynamical Poisson structure.

Contribution

It reveals that matrix-model actions for noncommutative U(n) gauge theories describe SU(n) gauge theory coupled to an emergent gravitational metric, providing a new framework for quantum gravity.

Findings

Coupling of gauge and scalar fields to an effective metric.

Recovery of gravitational wave degrees of freedom.

Potential for quantizing gravity within this framework.

Abstract

We show that the matrix-model action for noncommutative U(n) gauge theory actually describes SU(n) gauge theory coupled to gravity. This is elaborated in the 4-dimensional case. The SU(n) gauge fields as well as additional scalar fields couple to an effective metric G_{ab}, which is determined by a dynamical Poisson structure. The emergent gravity is intimately related to noncommutativity, encoding those degrees of freedom which are usually interpreted as U(1) gauge fields. This leads to a class of metrics which contains the physical degrees of freedom of gravitational waves, and allows to recover e.g. the Newtonian limit with arbitrary mass distribution. It also suggests a consistent picture of UV/IR mixing in terms of an induced gravity action. This should provide a suitable framework for quantizing gravity.