Carrollian approach to 1 + 3D flat holography

Abstract

The isomorphism between the (extended) BMS4 algebra and the 1 + 2D 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 + 2D Carrollian conformal symmetry. Motivated by this fact, we study the general symmetry properties of a source-less 1 + 2D Carrollian CFT, adopting a purely field-theoretic approach. After deriving the position-space Ward identities, we show how the 1 + 3D 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 0 ± , $$ {S}_1^{\pm } $$ S 1 ± , T and $$ \overline{T} $$ 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 0 + , $$ {S}_1^{+} $$ 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 Vir $$ \overset{\wedge }{\ltimes \overline{\textrm{sl}\left(2,{\mathbb{R}}\right)}} $$ ⋉ sl 2 ℝ ¯ ∧ with an abelian ideal.

Quantum Carroll/fracton particles

“…Carroll/fractons and flat space holography. Carrollian physics naturally emerges in the study of the asymptotic structure of spacetime in the absence of a cosmological constant (see, e.g., [16,17,[71][72][73][74][75][76][77]), due to the underlying equivalence between BMS and conformal Carroll algebras [71]. Although our work does not focus on the con-JHEP10(2023)041…”

Symmetry group at future null infinity II: Vector theory

“…Recently, the BMS group is identified as the so-called conformal Carroll group of level 2 [19][20][21] in the context of Carrollian manifold [22][23][24]. We may also study the representation of the BMS group [25,26] and construct field theories with Carrollian symmetry [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45]. However, the relation between the Carrollian field theory and the bulk theory is not straightforward in this method.…”

BMS modular covariance and structure constants

“…Carrollian holography, on the other hand, seems to be more natural from the point of view of the original ideas of holography and proposes a co-dimension one holographic dual where one not only uses the Lorentz sub-group of the Poincare group but fits translations naturally into the formulation [18]. Recent successes include [19][20][21][22][23][24]. The initial success of the formulation was in lower dimensions, specifically in understanding 3d asymptotically flat spacetime, which we describe below.…”