Momentum Space Correlation Functions in 2D Galilean Conformal Algebra

TL;DR

This paper develops the theory of momentum space correlation functions in 2D Galilean Conformal Algebra, deriving solutions to Ward identities and resolving Fourier transform issues through analytic continuation.

Contribution

It introduces a method to compute momentum space correlators in 2D GCA by solving Ward identities and analytically continuing boost eigenvalues.

Findings

Derived momentum space two-point and three-point functions.

Established the equivalence with position space correlators via analytic continuation.

Resolved Fourier transform existence issues in nonrelativistic conformal theories.

Abstract

Galilean Conformal Algebra (GCA) arises as a controlled nonrelativistic limit of the relativistic conformal algebra. In this paper, we initiate the study of momentum space correlation functions in two-dimensional GCA. We derive and solve momentum space Ward identities to obtain two-point and three-point functions. However, relating them to position space correlation functions presents a challenge as Fourier transforms of the latter do not exist. This is resolved by analytically continuing the boost eigenvalues to imaginary values. In this regime, the Fourier transform of the position space two-point and three-point functions exist and match exactly with the momentum space two-point and three-point function obtained by solving the Ward identities.