Carrollian Physics and Holography

This report reviews key developments in Carrollian physics with an emphasis on their role in the emerging framework of holography in asymptotically flat spacetimes. We begin by introducing the Carrollian limit, understood as the non-relativistic contraction of the Poincaré group obtained by formally taking the speed of light to zero. The geometric structures associated with this limit are described and argued to arise naturally on null hypersurfaces, most notably on null infinity, as well as black hole and cosmological horizons. Building on this, we examine the relation between the Bondi-Metzner-Sachs symmetries governing asymptotically flat gravity and the conformal Carrollian symmetries. Explicit examples of Carrollian field theories are constructed by implementing the limit on well-known relativistic field theories, with particular attention to Carrollian CFTs. We then present the Carrollian holography proposal, according to which gravity in asymptotically flat spacetimes is dual to a Carrollian CFT living at null infinity in one lower dimension. In this framework, the massless $\mathcal{S}$-matrix written in position space at null infinity is naturally reinterpreted in terms of boundary Carrollian CFT correlators, called Carrollian amplitudes. We highlight their relation to celestial amplitudes and show how they naturally emerge from holographic CFT correlators through a correspondence between the flat space limit in the bulk and the Carrollian limit at the boundary. Using this correspondence, we provide strong evidence that flat space holography arises from a controlled and consistent limiting procedure applied to both sides of the AdS/CFT duality. We conclude by outlining future directions and open questions in the program.

💡 Research Summary

The paper provides a comprehensive review of recent progress in Carrollian physics and its application to flat‑space holography. It begins by defining the Carrollian limit as the ultra‑non‑relativistic contraction of the Poincaré group obtained by sending the speed of light c to zero. The resulting Carroll group, its algebra, and the associated conformal extension are contrasted with the Galilean case. The authors then develop the geometric framework of Carrollian manifolds, introducing Ehresmann connections, Carrollian frames, and the notions of acceleration, vorticity, and shear that naturally live on null hypersurfaces. In particular, they show that null infinity—obtained via Penrose compactification—as well as black‑hole and cosmological horizons inherit an induced Carrollian geometry.

A central observation is the isomorphism between the Bondi‑Metzner‑Sachs (BMS) algebra governing asymptotically flat gravity and the conformal Carrollian algebra. This identification motivates the proposal that gravity in (d + 1)‑dimensional flat spacetime is dual to a d‑dimensional Carrollian conformal field theory (Carrollian CFT) living on null infinity. The authors construct explicit Carrollian field theories by taking the c → 0 limit of familiar relativistic models (scalar, Maxwell, Yang‑Mills, gravity, fermions, strings). They derive the Carrollian stress tensor, primary operators, Ward identities, and operator product expansions, emphasizing the ultra‑local nature of correlators (distributional low‑point functions).

The “Carrollian holography” proposal is then formulated: the flat‑space S‑matrix, written in position space at null infinity, is reinterpreted as correlators of the boundary Carrollian CFT, termed Carrollian amplitudes. These amplitudes are shown to be closely related to celestial amplitudes; soft theorems map to Ward identities of the Carrollian stress tensor, while collinear limits correspond to holomorphic Carrollian OPEs. The paper supplies concrete examples, Feynman rules, and differential equations governing Carrollian amplitudes.

A major achievement is the demonstration that the flat‑space limit of AdS/CFT (Λ → 0) corresponds precisely to the Carrollian limit on the boundary (c → 0). Taking this double limit converts Witten diagrams in AdS into Feynman diagrams for Carrollian amplitudes and matches the Carrollian limit of holographic CFT correlators. This correspondence reproduces known results such as the BMS₃ central charge, flat‑space entropy formulas, and the emergence of the Lw₁₊∞ algebra in four‑dimensional gravity.

Finally, the authors discuss open problems—modular properties of Carrollian CFTs, a complete quantum formulation, and the precise bridge to celestial holography—and outline future research directions. By unifying Carrollian physics, flat‑space holography, and celestial amplitudes, the work offers a coherent top‑down pathway from AdS/CFT to a systematic holographic description of our (asymptotically flat) universe.