Quantizing Carrollian field theories

TL;DR

This paper quantizes simple Carrollian field theories, revealing their ultraviolet sensitivity and showing they can be regulated on a lattice, leading to continuum models with generalized free field behavior and preserved supertranslation symmetry.

Contribution

It provides the first detailed quantization of two-derivative Carrollian theories, highlighting their unique ultraviolet properties and establishing a lattice regulation approach.

Findings

Carrollian theories are ultraviolet sensitive and require lattice regulation.

Lattice-regulated Carrollian theories retain important long-distance details.

Continuum limits yield generalized free fields with suppressed non-Gaussian correlations.

Abstract

Carrollian field theories have recently emerged as a candidate dual to flat space quantum gravity. We carefully quantize simple two-derivative Carrollian theories, revealing a strong sensitivity to the ultraviolet. They can be regulated upon being placed on a spatial lattice and working at finite inverse temperature. Unlike in conventional field theories, the details of the lattice-regulated Carrollian theories remain important at long distances even in the limit that the lattice spacing is sent to zero. We use that limit to define interacting continuum models with a tractable perturbative expansion. The ensuing theories are those of generalized free fields, with non-Gaussian correlations suppressed by positive powers of the lattice spacing, and an unbroken supertranslation symmetry.