Emergence of Conformal Invariance in Carrollian Field Theories

In the limit of vanishing speed of light, one is faced with field theories with Carrollian symmetry. When a Carrollian field theory acquires scale invariance it is automatically endowed with conformal invariance, provided that unitarity and locality hold. Using flat space holography we also obtain a c-function for this theory which is monotonically decreasing from the UV to the IR. This is done by invoking the null energy condition in the bulk.