Quantum Gravity at a Lifshitz Point

TL;DR

This paper proposes a quantum gravity theory with anisotropic scaling (z=3) in the UV, which flows to relativistic gravity at long distances, potentially serving as a UV completion of Einstein's general relativity.

Contribution

It introduces a power-counting renormalizable quantum gravity model with anisotropic scaling and explores its flow to relativistic gravity, connecting nonrelativistic and relativistic regimes.

Findings

The theory is power-counting renormalizable in 3+1 dimensions.

It flows from a nonrelativistic UV fixed point to relativistic IR behavior.

Emergent constants include the speed of light, Newton's constant, and the cosmological constant.

Abstract

We present a candidate quantum field theory of gravity with dynamical critical exponent equal to z=3 in the UV. (As in condensed matter systems, z measures the degree of anisotropy between space and time.) This theory, which at short distances describes interacting nonrelativistic gravitons, is power-counting renormalizable in 3+1 dimensions. When restricted to satisfy the condition of detailed balance, this theory is intimately related to topologically massive gravity in three dimensions, and the geometry of the Cotton tensor. At long distances, this theory flows naturally to the relativistic value z=1, and could therefore serve as a possible candidate for a UV completion of Einstein's general relativity or an infrared modification thereof. The effective speed of light, the Newton constant and the cosmological constant all emerge from relevant deformations of the deeply nonrelativistic z=3 theory at short distances.