Ghost wave-function renormalization in Asymptotically Safe Quantum Gravity

TL;DR

This paper explores the impact of ghost field wave-function renormalization on the renormalization group flow in asymptotically safe quantum gravity, revealing a non-trivial UV fixed point and effective two-dimensionality at short distances.

Contribution

It introduces ghost wave-function renormalization into the Einstein-Hilbert truncation, providing new insights into the fixed point structure of quantum gravity.

Findings

Identification of a non-trivial ultraviolet fixed point.

Ghost anomalous dimension at the fixed point is -1.8.

Fixed point persists with extra dimensions.

Abstract

Motivated by Weinberg's asymptotic safety scenario, we investigate the gravitational renormalization group flow in the Einstein-Hilbert truncation supplemented by the wave-function renormalization of the ghost fields. The latter induces non-trivial corrections to the beta-functions for Newton's constant and the cosmological constant. The resulting ghost-improved phase diagram is investigated in detail. In particular, we find a non-trivial ultraviolet fixed point in agreement with the asymptotic safety conjecture, which also survives in the presence of extra dimensions. In four dimensions the ghost anomalous dimension at the fixed point is $\eta_c^* = -1.8$, supporting space-time being effectively two-dimensional at short distances.