# Field Theories with Conformal Carrollian Symmetry

## TL;DR

This paper constructs explicit conformal Carrollian field theories as limits of relativistic conformal theories, revealing an infinite enhancement of symmetries and their potential as holographic duals to flat spacetime gravity.

## Contribution

It provides the first detailed construction of conformal Carrollian field theories from relativistic counterparts, including gauge theories and matter fields, highlighting their symmetry structures.

## Key findings

- Carrollian theories exhibit infinite symmetry enhancement in 4D.
- Explicit examples of Carrollian scalars, fermions, and gauge theories are constructed.
- These theories serve as holographic duals to asymptotically flat gravitational spacetimes.

## Abstract

Conformal Carrollian groups are known to be isomorphic to Bondi-Metzner-Sachs (BMS) groups that arise as the asymptotic symmetries at the null boundary of Minkowski spacetime. The Carrollian algebra is obtained from the Poincare algebra by taking the speed of light to zero, and the conformal version similarly follows. In this paper, we construct explicit examples of Conformal Carrollian field theories as limits of relativistic conformal theories, which include Carrollian versions of scalars, fermions, electromagnetism, Yang-Mills theory and general gauge theories coupled to matter fields. Due to the isomorphism with BMS symmetries, these field theories form prototypical examples of holographic duals to gravitational theories in asymptotically flat spacetimes. The intricacies of the limiting procedure lead to a plethora of different Carrollian sectors in the gauge theories we consider. Concentrating on the equations of motion of these theories, we show that even in dimensions d=4, there is an infinite enhancement of the underlying symmetry structure. Our analysis is general enough to suggest that this infinite enhancement is a generic feature of the ultra-relativistic limit that we consider.