Constructing Carrollian CFTs

TL;DR

This work builds scalar field theories directly on Carroll manifolds, enforcing diffeomorphism and Weyl invariance to obtain two main classes of equations—time-like and space-like—valid for general dynamical exponent $z$ and conformal weight $\delta$. It delivers explicit gauge-invariant actions and shows how monomial potentials constrain $z$ and $\delta$, while connecting special cases to the ultra-relativistic limit of conformally coupled scalars on Randers-Papapetrou backgrounds. Gauge fixing yields Carrollian CFTs with residual symmetry algebra $\mathfrak{cca}_3^{(z)}$, featuring the scalar $\Phi$ and an additional two-component field $b_i$, and reveals a rich structure of residual symmetries and potential holographic applications to flat space gravity. The results extend to higher dimensions and other matter fields, and open paths to quantum aspects, anomalies, and connections to BMS-type algebras and Galilean dualities.

Abstract

We construct classical theories for scalar fields in arbitrary Carroll spacetimes that are invariant under Carrollian diffeomorphisms and Weyl transformations. When the local symmetries are gauge fixed these theories become Carrollian conformal field theories. We show that generically there are at least two types of such theories: one in which only time derivatives of the fields appear and the other in which both space and time derivatives appear. A classification of such scalar field theories in three (and higher) dimensions up to two derivative order is provided. We show that only a special case of our theories arises in the ultra-relativistic limit of a covariant parent theory.