A note on graviton exchange in emergent gravity scenario

Understand

It is well-known that there exists a close relation between a large $N$ matrix model and noncommutative (NC) field theory: The latter can be naturally obtained from the former by expanding it around a specific background.

• Because the matrix model can be a constructive formulation of string theory, this relation suggests that NC field theory can also include quantum gravity.
• In particular, the NC $U(1)$ gauge theory attracts much attention because its low-energy effective action partially contains gravity where the metric is determined by the $U(1)$ gauge field.
• Thus, the NC $U(1)$ gauge theory could be a quantum theory of gravity.