[論文レビュー] Carrollian Physics and Holography

Romain Ruzziconi|arXiv (Cornell University)|Feb 2, 2026

Black Holes and Theoretical Physics被引用数 0

ひとこと要約

この論文は Carrollian 物理を検討し、Carrollian 場の理論を構築し、漸近的に平坦空間における重力の Carrollian ヒログラフィーを展開し、それを celestial ヒログラフィーおよび AdS/CFT の平坦空間極限と結びつける。

ABSTRACT

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.

研究の動機と目的

• Introduce the Carrollian limit as a c -> 0 contraction of the Poincaré group and contrast with Galilean physics.
• Develop Carrollian geometry and its natural appearance on null hypersurfaces such as null infinity.
• Construct and analyze Carrollian field theories and Carrollian CFTs, including Ward identities and OPEs.
• Propose and exemplify Carrollian holography for gravity in asymptotically flat spacetimes, defining Carrollian amplitudes.
• Explore the relation between Carrollian holography and celestial holography and the flat space limit from AdS/CFT.

提案手法

• Define the Carrollian limit and the associated Carrollian group and algebra.
• Develop Carrollian geometry including connections, Ehresmann structures, and induced geometry on null hypersurfaces.
• Obtain Carrollian field theories by taking c -> 0 limits of relativistic theories (scalar, Maxwell/Yang-Mills, gravity).
• Formulate Carrollian CFTs with primaries, Ward identities, stress-tensor correlators, and OPEs.
• Propose Carrollian holography: bulk gravity in flat space dual to a Carrollian CFT at null infinity and define Carrollian amplitudes.
• Explain the link to celestial holography and the flat space limit correspondence with AdS/CFT.]
• research_questions: ["What is the precise Carrollian limit and how does it differ from the Galilean limit?","How does Carrollian geometry encode null hypersurface structures and BMS symmetries?","How can one construct Carrollian field theories and Carrollian CFTs from relativistic theories?","What is the proper formulation of Carrollian holography and Carrollian amplitudes?","How do Carrollian amplitudes relate to celestial amplitudes and the flat space limit of AdS/CFT?"]
• key_findings:[

Figure 1: The causal structure can be represented by light cones. The effect of taking the Galilean limit is to open the light cones. In the limit, all spacetime events become causally connected.

実験結果

リサーチクエスチョン

• RQ1 What is the precise Carrollian limit and how does it differ from the Galilean limit?
• RQ2 How does Carrollian geometry encode null hypersurface structures and BMS symmetries?
• RQ3 How can one construct Carrollian field theories and Carrollian CFTs from relativistic theories?
• RQ4 What is the proper formulation of Carrollian holography and Carrollian amplitudes?
• RQ5 How do Carrollian amplitudes relate to celestial amplitudes and the flat space limit of AdS/CFT?

主な発見

• Carrollian physics naturally describes null hypersurfaces and aligns the conformal Carrollian algebra with BMS symmetries.
• Carrollian field theories and Carrollian CFTs can be realized as c -> 0 limits of relativistic theories, including stress-tensor structures and OPEs.
• A Carrollian holography program for four-dimensional flat space posits a dual Carrollian CFT at null infinity, encoding the bulk S-matrix as Carrollian amplitudes.
• There is a robust connection between Carrollian holography and celestial holography, with Carrollian amplitudes derived from flat space limits of holographic correlators.
• Flat space holography can be approached via a controlled limiting procedure from AdS/CFT, providing a pathway toward a top-down realization.

Figure 2: The effect of taking the Carrollian limit is to close the light cones. In the limit, all spacetime events become causally disconnected unless they are at the same spatial point. This reflects the ultra-local nature of Carrollian physics.