Noncommutative Spacetime and Emergent Gravity

TL;DR

This paper proposes that field theories on noncommutative spacetime naturally give rise to emergent gravity, linking noncommutative geometry, matrix models, and gravitational metrics through large N duality.

Contribution

It establishes a conceptual framework connecting noncommutative field theories with emergent gravity via matrix models and large N duality, highlighting the role of noncommutativity in gravity emergence.

Findings

Noncommutative spacetime acts as a phase space leading to emergent gravity.

Noncommutative fields can be identified with vector (tetrad) fields defining a gravitational metric.

Large N duality relates noncommutative gauge theories to emergent gravitational geometries.

Abstract

We argue that a field theory defined on noncommutative (NC) spacetime should be regarded as a theory of gravity, which we refer to as the emergent gravity. A whole point of the emergent gravity is essentially originated from the basic property: A NC spacetime is a (NC) phase space. This fact leads to two important consequences: (I) A NC field theory can basically be identified with a matrix model or a large N field theory where NC fields can be regarded as master fields of large N matrices. (II) NC fields essentially define vector (tetrad) fields. So they define a gravitational metric of some manifold as an emergent geometry from NC gauge fields. Of course, the pictures (I) and (II) should refer to the same physics, which should be familiar with the large N duality in string theory. The 1/N corrections in the picture (I) correspond to the derivative corrections in terms of the noncommutativity \theta for the picture (II).