Dimension and Dimensional Reduction in Quantum Gravity

TL;DR

This paper reviews evidence that quantum gravity exhibits effective two-dimensional behavior at short distances due to anomalous scaling at the ultraviolet fixed point, highlighting the universality of dimensional reduction.

Contribution

It synthesizes multiple lines of evidence for dimensional reduction in quantum gravity and discusses the physical meaning and possible mechanisms behind this universal phenomenon.

Findings

Multiple approaches indicate short-distance dimensional reduction.

Anomalous scaling at the UV fixed point suggests effective two-dimensionality.

Discussion of mechanisms explaining the universality of this behavior.

Abstract

If gravity is asymptotically safe, operators will exhibit anomalous scaling at the ultraviolet fixed point in a way that makes the theory effectively two-dimensional. A number of independent lines of evidence, based on different approaches to quantization, indicate a similar short-distance dimensional reduction. I will review the evidence for this behavior, emphasizing the physical question of what one means by `dimension' in a quantum spacetime, and will discuss possible mechanisms that could explain the universality of this phenomenon.