  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.
