# Lorentzian CFT 3-point functions in momentum space

## TL;DR

This paper computes Lorentzian momentum-space three-point functions in conformal field theories, extending known Euclidean results to Lorentzian signature and exploring applications like the ANEC operator.

## Contribution

It provides a formal Wick rotation method to derive Lorentzian correlators from Euclidean ones in arbitrary dimensions, including tensorial cases.

## Key findings

- Derived Lorentzian three-point functions in momentum space for scalar operators.
- Computed correlator involving two scalars and an energy-momentum tensor.
- Showed simplifications in ANEC operator expectation values using this approach.

## Abstract

In a conformal field theory, two and three-point functions of scalar operators and conserved currents are completely determined, up to constants, by conformal invariance. The expressions for these correlators in Euclidean signature are long known in position space, and were fully worked out in recent years in momentum space. In Lorentzian signature, the position-space correlators simply follow from the Euclidean ones by means of the i-epsilon prescription. In this paper, we compute the Lorentzian correlators in momentum space and in arbitrary dimensions for three scalar operators by means of a formal Wick rotation. We explain how tensorial three-point correlators can be obtained and, in particular, compute the correlator with two identical scalars and one energy-momentum tensor. As an application, we show that expectation values of the ANEC operator simplify in this approach.