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 AdS /CFT correspondence, which relates M-theory in AdS ×S to a certain superconformal Chern-Simons-matter theory known as the ABJM theory. In this limit, the boundary of AdS 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 AdS ×S and reducing along the S . We also present a general analysis of three-dimensional superconformal Carrollian symmetry.

United Kingdom

Arthur Lipstein

Romain Ruzziconi

Akshay Srikant

Towards a flat space Carrollian hologram from AdS

Carrollian amplitudes are flat space amplitudes written in position space at null infinity which can be re-interpreted as correlators in a putative dual Carrollian CFT. We argue that these amplitudes are the natural objects obtained in the flat space limit of AdS Lorentzian boundary correlators. The flat limit is taken entirely in position space by introducing Bondi coordinates in the bulk. From the bulk perspective, this procedure makes it manifest that the flat limit of any Witten diagram is the corresponding flat space Feynman diagram. It also makes explicit the fact that the flat limit in the bulk is implemented by a Carrollian limit at the boundary. We systematically analyse tree-level two, three and four-point correlators. Familiar features such as the distributional nature of Carrollian amplitudes and the presence of a bulk point singularity arise naturally as a consequence of requiring a finite and non-trivial Carrollian limit.

Luis Alday

Maria Nocchi

Akshay Yelleshpur Srikant

Carrollian amplitudes from holographic correlators

We show that the Ward identities of a Carrollian CFT stress tensor at null infinity reproduce the leading and subleading soft graviton theorems for massless scattering in the bulk. We deduce the expressions of the stress tensor components in terms of the bulk radiative modes, and these components turn out to be local at $$ \mathcal{I} $$ in terms of the twistor potentials. This analysis makes the correspondence between the large-time limit of Carrollian amplitudes and the soft limit of momentum space amplitudes manifest. We then construct Carrollian CFT currents from the ascendants of the hard graviton operator, which satisfy the algebra. We show that the large-time limit of their Ward identities implies an infinite tower of projected soft graviton theorems in the bulk, while their finite-time OPEs encode the collinear limit of scattering amplitudes.

India

Amartya Saha

Holographic Carrollian currents for massless scattering

The celestial Lw 1+∞  symmetries in asymptotically flat spacetimes have a natural geometric interpretation on twistor space in terms of Poisson diffeomorphisms. Using this framework, we provide a first-principle derivation of the canonical generators associated with these symmetries starting from the Poisson BF twistor action for self-dual gravity. We express these charges as surface integrals over the celestial sphere in terms of spacetime data at null infinity. The connection between twistor space and spacetime expressions at   <math> <mi>I</mi> </math>  $$ \mathcal{I} $$  is achieved via an integral formula for the asymptotic Bianchi identities due to Bramson and Tod. Finally, we clarify how Lw 1+∞  transformations are symmetries of gravity from a phase space perspective by showing the invariance of the asymptotic Bianchi identities.

Adam Kmec

Lionel Mason

Celestial Lw 1+∞ charges from a twistor action

Differential equations are powerful tools in the study of correlation functions in conformal field theories (CFTs). Carrollian amplitudes behave as correlation functions of Carrollian CFT that holographically describes asymptotically flat spacetime. We derive linear differential equations satisfied by Carrollian MHV gluon and graviton amplitudes. We obtain non-distributional solutions for both the gluon and graviton cases. We perform various consistency checks for these differential equations, including compatibility with conformal Carrollian symmetries.

Germany

Stephan Stieberger

Poland

United States

Tomasz Taylor

Bin Zhu

Differential equations for Carrollian amplitudes

We propose a consistent set of boundary conditions for gravity in asymptotically flat spacetime at spacelike infinity, which yields an enhancement of the Bondi-Metzner-Sachs group with smooth superrotations and new subleading symmetries. These boundary conditions are obtained by allowing fluctuations of the boundary structure which are responsible for divergences in the symplectic form, and a renormalization procedure is required to obtain finite canonical generators. The latter are then made integrable by incorporating boundary terms into the symplectic structure, which naturally derive from a linearized spin-two boundary field on a curved background with positive cosmological constant. Finally, we show that the canonical generators form a nonlinear algebra under the Poisson bracket and verify the consistency of this structure with the Jacobi identity.

Austria

Adrien Fiorucci

Spain

Javier Matulich

Superrotations at spacelike infinity

Carrollian holography aims to express gravity in four-dimensional asymptotically flat spacetime in terms of a dual three-dimensional Carrollian CFT living at null infinity. Carrollian amplitudes are massless scattering amplitudes written in terms of asymptotic or null data at   <math> <mi>I</mi> </math>  $$ \mathcal{I} $$ . These position space amplitudes at   <math> <mi>I</mi> </math>  $$ \mathcal{I} $$  are to be re-interpreted as correlation functions in the putative dual Carrollian CFT. We derive basic results concerning tree-level Carrollian amplitudes yielding dynamical constraints on the holographic dual. We obtain surprisingly compact expressions for n-point MHV gluon and graviton amplitudes in position space at   <math> <mi>I</mi> </math>  $$ \mathcal{I} $$ . We discuss the UV/IR behaviours of Carrollian amplitudes and investigate their collinear limit, which allows us to define a notion of Carrollian OPE. By smearing the OPE along the generators of null infinity, we obtain the action of the celestial symmetries — namely, the S algebra for Yang-Mills theory and Lw 1+∞  for gravity — on the Carrollian operators. As a consistency check, we systematically relate our results with celestial amplitudes using the link between the two approaches. Finally, we initiate a direct connection between twistor space and Carrollian amplitudes.

Carrollian amplitudes and celestial symmetries

Laura Donnay

Kevin Nguyen

Erratum to: Loop-corrected subleading soft theorem and the celestial stress tensor

Soft graviton theorems receive one-loop contributions that are logarithmic in the energy of the soft graviton, and which are closely related to tails of gravitational waveforms. We demonstrate that these logarithmic corrections are encoded in the Ward identity of superrotation symmetries, i.e. they follow from conservation of superrotation charge across spatial infinity i 0. Our proof relies on a careful analysis of the radiative phase space admitting such gravitational tails, and the determination of the fluxes through null infinity   <math> <mi>I</mi> </math>  $$ \mathcal{I} $$  that act as canonical generators of superrotations on both gravitational and matter fields. All logarithmic terms are derived from the fluxes through correlations of the supertranslation Goldstone mode, provided care is taken in manipulating gravitationally interacting (i.e. dressed) rather than free fields. In cases where massive particles take part in the scattering process, logarithmic corrections also partly arise from the superrotation charge generator at timelike infinity i  ± .

Italy

Shreyansh Agrawal

Logarithmic soft graviton theorems from superrotation Ward identities

Leaky boundary conditions in asymptotically AdS spacetimes are relevant to discuss black hole evaporation and the evolution of the Page curve via the island formula. We explore the consequences of leaky boundary conditions on the one-loop partition function of gravity. We focus on JT gravity minimally coupled to a scalar field whose normalizable and non-normalizable modes are both turned on, allowing for leakiness through the AdS boundary. Classically, this yields a flux-balance law relating the scalar news to the time derivative of the mass. Semi-classically, we argue that the usual diffeomorphism-invariant measure is ill-defined, suggesting that the area-non-preserving diffeomorphisms are broken at one loop. We calculate the associated anomaly and its implication on the gravitational Gauss law. Finally, we generalize our arguments to higher dimensions and dS.