The four-point correlation function of the energy-momentum tensor in the free conformal field theory of a scalar field

We present an explicit momentum space computation of the four-point function of the energy-momentum tensor in 4 spacetime dimensions for the free and conformally invariant theory of a scalar field. The result is obtained by explicit evaluation of the Feynman diagrams by tensor reduction. We work by embedding the scalar field theory in a gravitational background consistently with conformal invariance in order to derive all the terms the correlator consists of and all the Ward identities implied by the requirements of general covariance and anomalous Weyl symmetry. We test all these identities numerically in several kinematic configurations. Mathematica notebooks detailing the step-by-step computation are made publicly available through a GitHub repository. To the best of our knowledge, this is the first explicit result for the four-point correlation function of the energy-momentum tensor in a conformal and non supersymmetric field theory which is readily numerically evaluable in any kinematic configuration.