Fractal geometry of higher derivative gravity

TL;DR

This paper investigates the fractal nature of geometric structures in higher derivative quantum gravity by analyzing their scaling properties and calculating their fractal dimensions at microscopic scales.

Contribution

It introduces a method to determine the fractal dimensions of geometric operators in higher derivative quantum gravity through renormalization of composite operators.

Findings

Fractal dimensions of lengths, areas, and volumes are derived.

Geometric operators exhibit non-trivial scaling behavior.

Results provide insights into the microscopic structure of quantum spacetime.

Abstract

We determine the scaling properties of geometric operators such as lengths, areas, and volumes in models of higher derivative quantum gravity by renormalizing appropriate composite operators. We use these results to deduce the fractal dimensions of such hypersurfaces embedded in a quantum spacetime at very small distances.