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Carrollian Approach to $1+3$D Flat Holography
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abstract
The isomorphism between the (extended) BMS$_4$ algebra and the $1+2$D Carrollian conformal algebra hints towards a co-dimension one formalism of flat holography with the field theory residing on the null-boundary of the asymptotically flat space-time enjoying a $1+2$D Carrollian conformal symmetry. Motivated by this fact, we study the general symmetry properties of a source-less $1+2$D Carrollian CFT, adopting a purely field-theoretic approach. After deriving the position-space Ward identities, we show how the $1+3$D bulk super-translation and the super-rotation memory effects emerge from them, manifested by the presence of a temporal step-function factor in the same. Temporal-Fourier transforming these memory effect equations, we directly reach the bulk null-momentum-space leading and sub-leading soft graviton theorems. Along the way, we construct six Carrollian fields $S^\pm_0$, $S^\pm_1$, $T$ and $\bar{T}$ corresponding to these soft graviton fields and the Celestial stress-tensors, purely in terms of the Carrollian stress-tensor components. The 2D Celestial shadow-relations and the null-state conditions arise as two natural byproducts of these constructions. We then show that those six fields consist of the modes that implement the super-rotations and a subset of the super-translations on the quantum fields. The temporal step-function allows us to relate the operator product expansions (OPEs) with the operator commutation relations via a complex contour integral prescription. We deduce that not all of those six fields can be taken together to form consistent OPEs. So choosing $S^+_0$, $S^+_1$ and $T$ as the local fields, we form their mutual OPEs using only the OPE-commutativity property, under two general assumptions. The symmetry algebra manifest in these holomorphic-sector OPEs is then shown to be $\text{Vir}\ltimes\hat{\overline{\text{sl}(2,\mathbb{R})}}$ with an abelian ideal.
Forward citations
Cited by 17 Pith papers
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Carrollian Dictionary for Massive Particles at Null Infinity
Massive one-particle states are encoded on null infinity by projecting their momenta onto null frames, giving an isometric map into the complete Carrollian representation.
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Missing Descendants in the Carrollian Conformal Family
Including the missing K0 descendant chain completes Carrollian conformal representations and produces C2>0 sectors and two-point correlators fixed only up to functions of Carrollian invariants.
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Carrollian limit of NS-NS and Heterotic Supergravity
Ultra-relativistic expansion plus dilaton scaling produces finite covariant Carrollian NS-NS and heterotic supergravity actions, with trivializable Green-Schwarz for the 1-form and finite leading Riem^{2} α' corrections.
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Light and Shadow OPEs: A Carroll Symmetric Approach to Flat Holography
Translation symmetry alone fixes the scaling dimension and leading OPE coefficient for light-transformed Carrollian primaries, matching known graviton, gluon, and Einstein-Yang-Mills results.
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Scalar fields and 3D Flat Space Cosmologies
A direct bulk derivation of scalar quasi-normal modes in 3D flat space cosmologies is presented, using a hard-wall boundary condition and complex momenta, together with one-loop partition functions computed in simplif...
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Non-Lorentzian Supergravity and Kinematical Superalgebras
Supersymmetric extensions of extended kinematical algebras are classified via semigroup expansion, and non-degenerate Chern-Simons supergravity actions are constructed in three dimensions.
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Towards a Holographic dual of Carrollian BCFT
An end-of-the-world brane in 3d flat spacetime is shown to reduce spacetime symmetries to the boundary Carrollian conformal algebra, suggesting a flat-space analogue of AdS3/BCFT2 holography.
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Supersymmetric Twisted Carroll Theories
A 2+1-dimensional twisted Carroll superalgebra is realized from a 2+2-dimensional parent algebra, with new off-shell magnetic scalar and Abelian Yang-Mills theories whose fields are time-independent but propagate in space.
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Infinite towers of 2d symmetry algebras from Carrollian limit of 3d CFT
The Carrollian limit of CFT3 operator products yields towers of sl(2,C) blocks that reproduce conformally soft photon and graviton theorems and the S and w1+∞ celestial symmetry algebras.
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On Carrollian and Celestial Correlators in General Dimensions
Explicit two-, three-, and four-point Carrollian and celestial amplitudes for massless scalars in D dimensions, connected to the flat/Carrollian limit of AdS/CFT correlators.
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A finite Carrollian critical point
A double-scaled N to 0 limit of Carrollian vector models and Yang-Mills produces interacting Carrollian correlators with finite effective central charge and hyperscaling violation.
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Modular matrices of 2d Carrollian and warped CFTs
Explicit modular S and T matrices are derived for Carrollian (bms3) and warped CFT characters, with checks of S squared and unitarity.
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Carrollian superstring in the flipped vacuum
The Carrollian superstring in the flipped vacuum has a non-truncated spectrum with nonzero winding in the infinite-radius limit, and its three-point graviton amplitudes match tensile superstring results up to location...
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Carrollian bosonic supergravity at order $\alpha'$ and the universal cancellation of higher-curvature divergences
Four-derivative and higher pure-gravitational α' corrections to bosonic supergravity admit a finite Carrollian limit, with an explicit action and a universal finiteness criterion for Riem^N terms.
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Quantization of Carrollian fermions
A first interacting 4D Carrollian Yukawa theory is constructed, showing ultralocal fermion-scalar interactions and one-loop beta functions with mostly Gaussian fixed points.
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3D Carrollian gravity from 2D Euclidean symmetry
Post-Carroll-Newtonian Chern-Simons gravities are systematically obtained by semigroup-expanding 2D Euclidean B_k algebras, recovering known Carrollian models as subcases.
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Lectures on Carrollian Holography
Massless scattering amplitudes, including gravitons, can be recast as correlators of a carrollian conformal field theory on null infinity, but the non-perturbative bootstrap program remains incomplete.
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