Carrollian Conformal Theories in Momentum Space

TL;DR

This paper explores Carrollian conformal field theories in momentum space, solving Ward identities to reveal various analytic structures and novel logarithmic behaviors in correlators, highlighting differences from position space formulations.

Contribution

It provides explicit solutions to momentum space Ward identities for Carrollian CFTs, uncovering new analytic structures and logarithmic behaviors not seen in position space.

Findings

Different branches characterized by analytic structures in energies

Logarithmic behavior in three-point functions at specific dimensions

Connections between Carrollian limits and CFT correlators through scaling

Abstract

We consider the Carrollian conformal field theories involving scalar operators in the momentum representation. The momentum space Ward identities are explicitly solved to obtain the different branches of 2 and 3 point Carrollian conformal correlators in the momentum space. The different branches are characterized by different analytic structures in the Carrollian energies. For specific values of the conformal dimensions, the three-point functions in momentum space exhibit logarithmic behaviour. This has no analogue in position space and instead originates from singularities in the Fourier transform relating position and momentum space correlators. We also analyze the Carrollian limit of CFT 2 and 3 point functions of scalar operators in momentum space. By taking different scalings of CFT correlators with respect to the speed of light, we obtain different branches of the Carrollian conformal correlators in the momentum space.