An embedding space approach to Carrollian CFT correlators for flat space holography

Abstract

Carrollian conformal field theories (carrollian CFTs) are natural field theories on null infinity of an asymptotically flat spacetime or, more generally, geometries with conformal carrollian structure. Using a basis transformation, gravitational S-matrix elements can be brought into the form of correlators of a carrollian CFT. Therefore, it has been suggested that carrollian CFTs could provide a co-dimension one dual description to gravity in asymptotically flat spacetimes. In this work, we construct an embedding space formalism for three-dimensional carrollian CFTs and use it to determine two- and three-point correlators. These correlators are fixed by the global subgroup, ISO(1, 3), of the carrollian conformal symmetries, i.e., the Bondi-van der Burg-Metzner-Sachs symmetries (BMS). The correlators coincide with well-known two- and three-point scattering amplitudes in Minkowski space written with respect to a basis of asymptotic position states.

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…”

The ambient space formalism

“…First put on paper by de Boer and Solodukhin [104,105], more recently it has been leveraged in several different contexts including [106][107][108]. In [109] an embedding space formalism on R 4,2 was also developed to find the form of Carrollian 2and 3-point functions up to spin 1.…”

Carrollian conformal correlators and massless scattering amplitudes

“…In the standard approach to scattering amplitudes, this issue is circumvented by the fact that virtual cubic interactions happen offshell. One potential way around this issue within a strictly onshell formalism is to consider complex momenta, i.e., to analytically continue the celestial sphere R d−1 to C d−1 in order to give non-vanishing support to the three-point scattering amplitude and corresponding Carrollian correlator [35]. We hope to come back to this point in a future publication.…”

“…Proceeding by analogy with standard conformal field theory, we then want to classify the two-and three-point correlation functions allowed by Poincaré symmetry. For d = 3 the two-point functions were classified in [28,35] while an incomplete set of three-point functions has been described in [35,36]. See also [24,37] for earlier discussions.…”