Romain Ruzziconi

A bstract: We construct in detail the irreducible representations of the BMS group with super rotations in three and four dimensions that have the same rest frame momenta as the massive and massless Poincaré point particles. We compare these representations to those of the Poincaré group and also to the analogous representations of global BMS. We argue that these extended BMS representations are carried by a string rather than a point particle. The super rotations play a crucial role in our discussions.

Pursuing our analysis of the companion Letter, [Celestial symmetries of black hole horizons, .], we study the gravitational solution space around a null hypersurface in the bulk of spacetime, such as a black hole or a cosmological horizon. We discuss the corresponding characteristic initial value problem both in the metric and Newman-Penrose formalisms and establish an explicit dictionary between the two. This allows us to identify Weyl-covariant structures in the solution space, including hierarchies of recursion relations encoding the flux-balance laws. We then establish a correspondence between the gravitational phase space at null infinity and the subleading phase space around the null hypersurface at finite distance. This connection is naturally formulated within the Newman-Penrose formalism by performing a partially off-shell conformal compactification and identifying the analog of the Ashtekar-Streubel symplectic structure in the radial expansion near the null hypersurface. Using this framework, we identify the celestial L w 1 + ∞ symmetries in the subleading phase space at finite distance by constructing their canonical generators and imposing self-duality conditions. This allows us to define a notion of covariant radiation, whose absence gives rise to an infinite tower of conserved charges, revealing physical quantities relevant to observers near black hole or cosmological horizons. As a concrete illustration, we consider the case of the self-dual Taub-Newman-Unti-Tamburino black hole.

We establish a correspondence between the gravitational phase space at null infinity and the subleading phase space near a finite-distance null hypersurface, such as a black hole horizon. Within this framework, we identify the celestial L w 1 + ∞ symmetries in the subleading phase space at the horizon by constructing their canonical generators and imposing self-duality conditions. This leads to an infinite tower of conserved charges in the absence of radiation, revealing new gravitational observables relevant to black hole physics.

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.

A bstract: Carrollian holography is a framework for flat space holography, suggesting that gravity in asymptotically flat spacetime in D dimensions is dual to a conformal Carrollian field theory in D – 1 dimensions living at null infinity. In this work, we elaborate on the definition of Carrollian amplitudes for massless scalar fields in general dimensions and provide explicit expressions for the two-, three-, and four-point functions. We show that these amplitudes naturally arise from Lorentzian holographic correlators in AdS/CFT through a correspondence between the flat space limit in the bulk and the Carrollian limit at the boundary. Finally, we use the relation between Carrollian and celestial holography to derive explicit expressions for celestial amplitudes in D dimensions, which are reinterpreted as correlators of the celestial CFT in D − 2 dimensions.

Finding a concrete example holography in four dimensional asymptotically flat space is an important open problem. A natural strategy is to take the flat space limit of the celebrated AdS₄/CFT₃ correspondence, which relates M-theory in AdS₄×S⁷ to a certain superconformal Chern-Simons-matter theory known as the ABJM theory. In this limit, the boundary of AdS₄ becomes null infinity and the ABJM theory should exhibit an emergent superconformal Carrollian symmetry. We investigate this possibility by matching the Carrollian limit of ABJM correlators with four-dimensional supergravity amplitudes that arise from taking the flat space limit of AdS₄×S⁷ and reducing along the S⁷. We also present a general analysis of three-dimensional superconformal Carrollian symmetry.