Asymptotically Safe Hilbert-Palatini Gravity in an On-Shell Reduction Scheme

TL;DR

This paper investigates the renormalization flow of Hilbert-Palatini gravity, providing evidence for an asymptotically safe high-energy completion with a fixed point similar to quantum Einstein gravity, using an on-shell reduction scheme.

Contribution

It introduces an on-shell reduction scheme to analyze Hilbert-Palatini gravity's renormalization flow, revealing a fixed point akin to the Reuter fixed point with distinct properties.

Findings

Existence of an ultraviolet fixed point similar to Reuter fixed point.

Differences from Einstein gravity are parametrized by an abelian gauge field.

Fixed point occurs at a smaller Newton coupling with more stable exponents.

Abstract

We study the renormalization flow of Hilbert-Palatini gravity to lowest non-trivial order. We find evidence for an asymptotically safe high-energy completion based on the existence of an ultraviolet fixed point similar to the Reuter fixed point of quantum Einstein gravity. In order to manage the quantization of the large number of independent degrees of freedom in terms of the metric as well as the connection, we use an on-shell reduction scheme: for this, we quantize all degrees of freedom beyond Einstein gravity at a given order that remain after using the equations of motion at the preceding order. In this way, we can straightforwardly keep track of the differences emerging from quantizing Hilbert-Palatini gravity in comparison with Einstein gravity. To lowest non-trivial order, the difference is parametrized by fluctuations of an additional abelian gauge field. The critical properties of the ultraviolet fixed point of Hilbert-Palatini gravity are similar to those of the Reuter fixed point, occurring at a smaller Newton coupling and exhibiting more stable higher order exponents.