# Impact of topology in foliated Quantum Einstein Gravity

## TL;DR

This paper investigates how the topology of spacetime influences the renormalization group flow in Quantum Einstein Gravity, finding a robust fixed point that supports the asymptotic safety scenario across different topologies.

## Contribution

It demonstrates that the renormalization group flow and fixed points are largely independent of the background topology in foliated Quantum Einstein Gravity.

## Key findings

- Existence of a non-trivial fixed point supporting asymptotic safety.
- Fixed point is stable under different parametrizations and regulators.
- Flow behavior is consistent across different background topologies.

## Abstract

We use a functional renormalization group equation tailored to the Arnowitt-Deser-Misner formulation of gravity to study the scale-dependence of Newton's coupling and the cosmological constant on a background spacetime with topology S^1xS^d. The resulting beta functions possess a non-trivial renormalization group fixed point, which may provide the high-energy completion of the theory through the asymptotic safety mechanism. The fixed point is robust with respect to changing the parametrization of the metric fluctuations and regulator scheme. The phase diagrams show that this fixed point is connected to a classical regime through a crossover. In addition the flow may exhibit a regime of "gravitational instability", modifying the theory in the deep infrared. Our work complements earlier studies of the gravitational renormalization group flow on a background topology S^1xT^d and establishes that the flow is essentially independent of the background topology.