Beta Function and Asymptotic Safety in Three-dimensional Higher Derivative Gravity

TL;DR

This paper investigates the quantum behavior of three-dimensional higher derivative gravity, demonstrating the existence of fixed points and confirming the theory's asymptotic safety through analysis of coupling flows.

Contribution

It provides the first detailed calculation of the running of gravitational and cosmological constants in 3D higher derivative gravity, establishing asymptotic safety and clarifying the role of fixed points.

Findings

Existence of Gaussian and nontrivial fixed points confirming asymptotic safety.

Fixed point value of the cosmological constant is gauge-independent, positive, and small.

New massive gravity and $f(R)$ gravity do not correspond to these fixed points.

Abstract

We study the quantum properties of the three-dimensional higher derivative gravity. In particular we calculate the running of the gravitational and cosmological constants. The flow of these couplings shows that there exist both Gaussian and nontrivial fixed points in the theory, thus confirming that the theory is asymptotically safe. It is shown that the new massive gravity or $f(R)$ gravity in three dimensions do not correspond to the fixed point within the approximation that the coefficients of the higher curvature terms are not subject to the flow. The fixed point value of the cosmological constant is found to be gauge-independent, positive and small. We also find that if we start with Einstein term with negative sign, the fixed point only exists when the coefficient of the Einstein term has positive sign.