# $d=4$ as the critical dimensionality of asymptotically safe interactions

## TL;DR

This paper investigates why our universe has four dimensions by examining asymptotically safe quantum gravity, suggesting that four dimensions are uniquely suited for safe interactions, especially regarding the Standard Model's $U(1)$ Landau pole problem.

## Contribution

It proposes that four dimensions are singled out as the critical dimensionality for asymptotically safe interactions, linking quantum gravity to the universe's dimensionality.

## Key findings

- Asymptotically safe quantum fluctuations can address the $U(1)$ Landau pole problem in four dimensions.
- Four dimensions may be uniquely compatible with asymptotic safety in fundamental interactions.
- The universe's four-dimensional structure could be a consequence of asymptotic safety constraints.

## Abstract

We explore the question why our universe is four dimensional from an asymptotically safe vantage point. We find hints that asymptotically safe quantum fluctuations of gravity can only solve the $U(1)$ Landau-pole problem in the Standard Model in four dimensions. This could single out the observed dimensionality of the universe as the critical dimensionality of asymptotically safe interactions.