A Carroll-covariant energy-momentum-news complex at future null infinity yields Ward identities that generalise the Bondi loss equations, with an anomalous Carroll boost.
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Nguyen, Lectures on Carrollian Holography, (2025), arXiv:2511.10162 [hep-th]
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abstract
Carrollian Holography aims to provide a holographic description of quantum gravity in asymptotically flat spacetimes, in terms of a novel kind of `carrollian' conformal field theory defined on the spacetime null conformal boundary $\mathscr{I}$. The goal of these lectures is to offer a self-contained, pedagogical introduction to this active field of research. The main focus is given to the correspondence between massless scattering amplitudes, including gravitational amplitudes, and correlators in carrollian conformal field theory. Strong emphasis is put on the development of carrollian conformal field theory as an intrinsic, independent, and non-perturbative framework in which to formulate gravitational scattering theory.
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The NLO/NNLO small-c (Carroll) expansion of GR admits a rich stationary vacuum sector with rotating Lense-Thirring-type, C-metric-type, Hartle-Thorne-type, and higher-multipole solutions, going beyond the static magnetic Carroll truncation.
Free Carrollian quantum field theories admit well-defined vacuum and KMS states via algebraic methods, with massless theories requiring nonregular states whose Hilbert spaces factorize into Fock and nonseparable zero-mode sectors relevant for flat space holography.
Finite Carrollian black-hole thermodynamics arises as a double-scaled low-temperature large-N ensemble in AdS/CFT, with the boundary Brown-York stress tensor reproducing the contracted bulk Hamiltonian and first law.
Recovers Minkowski massless integer-spin solution space as smooth limit of AdS solution space for even dimensions via cosmological-constant expansion of source and vev.
Carrollian fermionic actions for electric and magnetic sectors are derived from a single Bargmann Dirac action by null reduction, with good and bad fermions as dynamical and constrained modes valid in any dimension.
The c to zero limit of ABJM theory produces a Carrollian superconformal theory with extended BMS4 symmetry using Carrollian Dirac matrices.
A Carrollian theory on null infinity reproduces all MHV and NMHV Yang-Mills tree amplitudes, with a new explicit NMHV expression.
Loop-level Carrollian amplitudes in N=4 SYM and N=8 supergravity are differential operators on tree-level versions, with logarithmic eikonal behavior and IR-safe factorization via natural splitting.
A path integral with asymptotic boundary conditions produces the gravitational S-matrix and derives soft graviton theorems from extended BMS symmetry Ward identities.
Carroll hydrodynamics with spin is obtained as the c→0 limit of relativistic hydrodynamics with spin, extending the description of boost-invariant flows.
The work identifies a broader class of 2D Carrollian CFT correlators that encode massive 3D Minkowski S-matrices and constructs the corresponding bulk-to-boundary propagator.
Double-scaling contractions of extended AdS black-hole thermodynamics produce finite Carrollian phase-space first laws with pressure-volume contributions under the condition α + γ = 1.
Bulk local states are built in flat holography via induced representations, with a dual basis resolving 3D bra-ket scaling issues and a tilde basis enabling explicit constructions in higher dimensions that recover the massive propagator.
A square-root T-bar-T deformation of 2D scalar fields carries the theory from relativistic conformal to Carrollian conformal, producing a new nonlinear 'magnetic' Carroll action at one end of the flow.
The angle-averaged soft and Goldstone modes of 4D asymptotically flat gravity are symplectically identified with the radial-size and area-edge modes of a spherically symmetric Minkowski causal diamond.
An agentic AI workflow constructs Carrollian conformal bases for massive and tachyonic particles via a Poincare-Carrollian intertwiner that requires complex momentum shifts.
citing papers explorer
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The Energy-Momentum-News Complex near Future Null Infinity
A Carroll-covariant energy-momentum-news complex at future null infinity yields Ward identities that generalise the Bondi loss equations, with an anomalous Carroll boost.
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Stationary solutions in the small-$c$ expansion of GR
The NLO/NNLO small-c (Carroll) expansion of GR admits a rich stationary vacuum sector with rotating Lense-Thirring-type, C-metric-type, Hartle-Thorne-type, and higher-multipole solutions, going beyond the static magnetic Carroll truncation.
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Carrollian quantum states and flat space holography
Free Carrollian quantum field theories admit well-defined vacuum and KMS states via algebraic methods, with massless theories requiring nonregular states whose Hilbert spaces factorize into Fock and nonseparable zero-mode sectors relevant for flat space holography.
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Large-$N$ Carrollian Thermodynamics from AdS Black-Hole Phase-Space Contractions
Finite Carrollian black-hole thermodynamics arises as a double-scaled low-temperature large-N ensemble in AdS/CFT, with the boundary Brown-York stress tensor reproducing the contracted bulk Hamiltonian and first law.
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Flat from AdS: in any dimension and for any spin
Recovers Minkowski massless integer-spin solution space as smooth limit of AdS solution space for even dimensions via cosmological-constant expansion of source and vev.
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Carroll fermions from null reduction: A case of good and bad fermions
Carrollian fermionic actions for electric and magnetic sectors are derived from a single Bargmann Dirac action by null reduction, with good and bad fermions as dynamical and constrained modes valid in any dimension.
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Carrollian ABJM: Fermions and Supersymmetry
The c to zero limit of ABJM theory produces a Carrollian superconformal theory with extended BMS4 symmetry using Carrollian Dirac matrices.
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Towards a Carrollian Description of Yang-Mills
A Carrollian theory on null infinity reproduces all MHV and NMHV Yang-Mills tree amplitudes, with a new explicit NMHV expression.
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On Carrollian Loop Amplitudes for Gauge Theory and Gravity
Loop-level Carrollian amplitudes in N=4 SYM and N=8 supergravity are differential operators on tree-level versions, with logarithmic eikonal behavior and IR-safe factorization via natural splitting.
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The gravitational S-matrix from the path integral: asymptotic symmetries and soft theorems
A path integral with asymptotic boundary conditions produces the gravitational S-matrix and derives soft graviton theorems from extended BMS symmetry Ward identities.
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Carroll hydrodynamics with spin
Carroll hydrodynamics with spin is obtained as the c→0 limit of relativistic hydrodynamics with spin, extending the description of boost-invariant flows.
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Massive fields in 3D Minkowski space and boundary correlators
The work identifies a broader class of 2D Carrollian CFT correlators that encode massive 3D Minkowski S-matrices and constructs the corresponding bulk-to-boundary propagator.
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Phase-Space Contractions of Carrollian Black-Hole Thermodynamics
Double-scaling contractions of extended AdS black-hole thermodynamics produce finite Carrollian phase-space first laws with pressure-volume contributions under the condition α + γ = 1.
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More on Bulk Local State Reconstruction in Flat/Carr CFT
Bulk local states are built in flat holography via induced representations, with a dual basis resolving 3D bra-ket scaling issues and a tilde basis enabling explicit constructions in higher dimensions that recover the massive propagator.
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On $\sqrt{T\overline{T}}$ deformed pathways: CFT to CCFT
A square-root T-bar-T deformation of 2D scalar fields carries the theory from relativistic conformal to Carrollian conformal, producing a new nonlinear 'magnetic' Carroll action at one end of the flow.
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From Asymptotically Flat Gravity to Finite Causal Diamonds
The angle-averaged soft and Goldstone modes of 4D asymptotically flat gravity are symplectically identified with the radial-size and area-edge modes of a spherically symmetric Minkowski causal diamond.
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Carrollian holography with agentic AI: Real mass is imaginary
An agentic AI workflow constructs Carrollian conformal bases for massive and tachyonic particles via a Poincare-Carrollian intertwiner that requires complex momentum shifts.
- Topics in Celestial holography: A bottom-up perspective