Carrollian Approach to $1+3$D Flat Holography

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 $S_0^{\pm }$, $S_1^{\pm }$, $T$ 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 $\text{Vir}⋉\widehat{\overline{\text{sl}(2,\mathbb{R})}}$ with an abelian ideal.

Section 3.3 is revised and contains a new result. Added references

References in corpus (10)

• Asymptotic symmetries and subleading soft graviton theorem
• Flat Holography: Aspects of the dual field theory
• Entropy of three-dimensional asymptotically flat cosmological solutions
• New symmetries for the Gravitational S-matrix
• 4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
• Entanglement entropy in Galilean conformal field theories and flat holography
• Conformal Carroll groups
• Sub-subleading Soft Graviton Theorem in Generic Theories of Quantum Gravity
• Massless Scalars and Higher-Spin BMS in Any Dimension
• Non-Lorentzian Kač-Moody Algebras

Cited by in corpus (26)

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• Super-Carrollian and Super-Galilean Field Theories
• Symmetry group at future null infinity II: Vector theory
• Carrollian Supersymmetry and SYK-like models
• Carroll Hawking effect
• Quantization of Carrollian conformal scalar theories
• Extended Kinematical 3D Gravity Theories
• Irrelevant and marginal deformed BMS field theories
• Radiation in Fluid/Gravity and the Flat Limit
• Bulk Reconstruction of Scalar Excitations in Flat${}_3$/CCFT${}_2$ and the Flat Limit from (A)dS${}_3$/CFT${}_2$
• Asymptotic Limit of Null Hypersurfaces
• Quantization of Carrollian fermions
• Carroll spinors
• Non-Lorentzian Supergravity and Kinematical Superalgebras
• Hydrodynamics in the Carrollian regime
• Carroll-Schrödinger Equation
• Celestial Eikonal Amplitudes in the Near-Horizon Region
• Loop corrections versus marginal deformation in celestial holography
• Universal sectors of two-dimensional Carrollian CFTs
• AdS${}_3$ Carroll gravity: asymptotic symmetries and C-thermal configurations
• Modular matrices of 2d Carrollian and warped CFTs
• CFT reconstruction of local bulk operators in half-Minkowski space