Field Theories with Conformal Carrollian Symmetry
Arjun Bagchi, Aditya Mehra, Poulami Nandi
TL;DR
This work constructs Conformal Carrollian Field Theories (CCFTs) by performing an ultra-relativistic contraction of relativistic conformal field theories, yielding explicit Carrollian counterparts for scalars, fermions, electrodynamics, and Yang–Mills theories with massless matter. It demonstrates that, in d=4, the equations of motion in these theories exhibit an infinite enhancement of symmetry, extending the finite Conformal Carrollian Algebra (CCA) to an infinite-dimensional structure, with an explicit lift in the supertranslation sector. The CCFTs are shown to be isomorphic to Bondi–Metzner–Sachs (BMS) symmetries, positioning them as prototypical holographic duals to gravitational theories in asymptotically flat spacetimes and highlighting flat-space holography as a fertile arena for new integrable sectors and constraints on dynamics. The paper systematically analyzes a wide array of sectors across Abelian and non-Abelian gauge theories, including Yukawa couplings, and discusses the implications for holography, tensionless limits, and potential action principles for these exotic theories. Overall, the results indicate that infinite Carrollian symmetries are a generic feature of ultra-relativistic limits of conformal field theories and may play a central role in flat-space holography and related high-energy limits.
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.