Conformal Carroll Scalars with Boosts

TL;DR

This paper develops two new conformal Carroll scalar field theories with local boost symmetry on curved backgrounds, providing explicit models that connect to celestial holography and Euclidean CFTs.

Contribution

It introduces two types of conformal Carroll scalar actions with boost invariance on curved backgrounds, expanding the set of explicit models in this area.

Findings

Energy-momentum tensors are traceless in both theories.

One theory type is dominated by time derivatives, the other by spatial derivatives.

Spatial conformal Carroll theories can be reduced to lower-dimensional Euclidean CFTs.

Abstract

We construct two distinct actions for scalar fields that are invariant under local Carroll boosts and Weyl transformations. Conformal Carroll field theories were recently argued to be related to the celestial holography description of asymptotically flat spacetimes. However, only few explicit examples of such theories are known, and they lack local Carroll boost symmetry on a generic curved background. We derive two types of conformal Carroll scalar actions with boost symmetry on a curved background in any dimension and compute their energy-momentum tensors, which are traceless. In the first type of theories, time derivatives dominate and spatial derivatives are suppressed. In the second type, spatial derivatives dominate, and constraints are present to ensure local boost invariance. By integrating out these constraints, we show that the spatial conformal Carroll theories can be reduced to lower-dimensional Euclidean CFTs, which is reminiscent of the embedding space construction.