Constructing Carrollian Field Theories from Null Reduction

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.

Section: Jhep06(2023)051mentioning

confidence: 99%

Carrollian approach to 1 + 3D flat holography

Saha

2023

“…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.…”

Section: Jhep07(2023)152mentioning

confidence: 99%

Symmetry group at future null infinity II: Vector theory

Liu

Long

2023

In this paper, we reduce the electromagnetic theory to future null infinity and obtain a vector theory at the boundary. We compute the Poincaré flux operators which could be generalized. We quantize the vector theory, and impose normal order on the extended flux operators. It is shown that these flux operators generate the supertranslation and superrotation. When work out the commutators of these operators, we find that a generalized electromagnetic duality operator should be included as the generators to form a closed symmetry algebra.

“…Our method may provide new insight to flat space holography [20][21][22][23][24][25][26][27][28][29][30][31][32] and to constructing more physically interesting Carrollian field theories [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49]. In this work, we will explore the boundary theory for Einstein gravity.…”

Section: Jhep10(2023)117mentioning

confidence: 99%

Symmetry group at future null infinity III: Gravitational theory

Liu,

Long

2023

We reduce the gravitational theory in an asymptotically flat spacetime to future null infinity. We compute the Poincaré flux operators at future null infinity and construct the supertranslation and superrotation generators. The generators are shown to form a closed symmetry algebra by including a generalized gravitational duality operator. We could regard all the generators as the Hamiltonians with respect to the symmetry transformation in the boundary field theory. Our construction of the generators may relate to the BMS fluxes defined in the literature by adding counterterms to the Bondi mass and angular momentum aspects.