Emergent Gravity, Matrix Models and UV/IR Mixing

TL;DR

This paper demonstrates that UV/IR mixing in noncommutative gauge theories can be interpreted as an emergent gravity effect, specifically deriving the Einstein-Hilbert action from matrix models through scalar field integration.

Contribution

It explicitly connects UV/IR mixing in noncommutative gauge theory to emergent gravity within matrix models, deriving gravity actions from field integrations.

Findings

UV/IR mixing corresponds to an induced gravity effect.

The Einstein-Hilbert action is derived from matrix models.

Gravity appears as an IR phenomenon due to UV/IR mixing.

Abstract

We verify explicitly that UV/IR mixing for noncommutative gauge theory can be understood in terms of an induced gravity action, as predicted by the identification [1] of gravity within matrix models of NC gauge theory. More precisely, we obtain the Einstein-Hilbert action by integrating out a scalar field in the adjoint. It arises from the well-known UV/IR mixing of NC gauge theory, which is carefully re-analyzed and interpreted in terms of gravity. The matrix model therefore contains gravity as an IR effect, due to UV/IR mixing.