# Momentum space approach to crossing symmetric CFT correlators II: General spacetime dimension

## TL;DR

This paper extends a momentum space framework for crossing symmetric conformal four-point functions from 3D to arbitrary dimensions, utilizing spherical harmonics to handle tensor structures.

## Contribution

It generalizes a previously developed 3D momentum space basis for scalar correlators to all spacetime dimensions, incorporating tensor techniques.

## Key findings

- Constructed a general dimensional crossing symmetric basis
- Utilized spherical harmonics for tensor correlators
- Enhanced understanding of conformal correlators in momentum space

## Abstract

Our previous work [1] constructed, in three-dimensional momentum space, a manifestly crossing symmetric basis for scalar conformal four-point functions, based on the factorization property proposed by Polyakov. This work extends this construction to general dimensional conformal field theory. To facilitate the treatment of symmetric traceless tensors, we exploit techniques of spherical harmonics in general dimensions.