Carrollian Approach to $1+3$D Flat Holography

Understand

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.