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 leads 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.
Highlights
1.1 Effective theories and singular limitsPhysics is all about length scales, and most theories that we use to describe Nature are effective theories, including the spectacularly successful Standard Model of particle physics
Conformal Carrollian groups are known to be isomorphic to Bondi-MetznerSachs (BMS) groups that arise as the asymptotic symmetries at the null boundary of Minkowski spacetime
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
Summary
Physics is all about length scales, and most theories that we use to describe Nature are effective theories, including the spectacularly successful Standard Model of particle physics. One could ask if similar new structures may emerge when one takes the speed of light to go to zero instead of infinity. This peculiar c → 0 limit has been dubbed the Carrollian limit in literature [17]. Mathematical curiosity is perhaps not very good justification for research in theoretical physics, many very important breakthroughs, like the formulation of Yang-Mills theories that later have led to the understanding of the weak and strong nuclear forces, have come via this path. Our investigations in this paper are driven by some very strong motivations, which we elaborate on below
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