Renormalization of quantum gravity coupled with matter in three dimensions

TL;DR

This paper investigates whether three-dimensional quantum gravity coupled with matter remains finite after quantum corrections, finding that divergences appear at two loops, indicating non-finiteness in this scenario.

Contribution

The study provides an explicit two-loop calculation showing divergences in quantum gravity with matter in three dimensions, challenging assumptions of finiteness.

Findings

Divergences appear at two-loop order in the coupled theory.

Finiteness does not hold when matter is coupled to 3D quantum gravity.

Four-fermion divergent vertices are generated by quantum corrections.

Abstract

In three spacetime dimensions, where no graviton propagates, pure gravity is known to be finite. It is natural to inquire whether finiteness survives the coupling with matter. Standard arguments ensure that there exists a subtraction scheme where no Lorentz-Chern-Simons term is generated by radiative corrections, but are not sufficiently powerful to ensure finiteness. Therefore, it is necessary to perform an explicit (two-loop) computation in a specific model. I consider quantum gravity coupled with Chern-Simons U(1) gauge theory and massless fermions and show that renormalization originates four-fermion divergent vertices at the second loop order. I conclude that quantum gravity coupled with matter, as it stands, is not finite in three spacetime dimensions.