On the stability of renormalizable expansions in three-dimensional gravity

TL;DR

This paper investigates the stability of 1/N expansions in three-dimensional gravity with matter fields, revealing tachyonic instabilities and proposing models with potential stability and fixed points.

Contribution

It analyzes the stability of renormalizable 1/N expansions in 3D gravity with matter, proposing models that may avoid instabilities and possess ultraviolet fixed points.

Findings

Tachyonic poles appear in the graviton propagator with unitary matter.

Introducing higher-derivative terms can eliminate tachyons.

Non-minimal scalar couplings may stabilize the model.

Abstract

Preliminary investigations are made for the stability of the $1/N$ expansion in three-dimensional gravity coupled to various matter fields, which are power-counting renormalizable. For unitary matters, a tachyonic pole appears in the spin-2 part of the leading graviton propagator, which implies the unstable flat space-time, unless the higher-derivative terms are introduced. As another possibility to avoid this spin-2 tachyon, we propose Einstein gravity coupled to non-unitary matters. It turns out that a tachyon appears in the spin-0 or -1 part for any linear gauges in this case, but it can be removed if non-minimally coupled scalars are included. We suggest an interesting model which may be stable and possess an ultraviolet fixed point.