Dimension and Dimensional Reduction in Quantum Gravity

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.Comment: For proceedings of the conference in honor of Martin Reuter: "Quantum Fields---From Fundamental Concepts to Phenomenological Questions"; 14 pages; based in part on my review article arXiv:1705.0541