Energy momentum tensor on and off the light cone: exposition with scalar Yukawa theory

We compute the gravitational form factors Aᵢ, Dᵢ and cᵢ of the scalar Yukawa theory using both the light-cone and covariant perturbation theory at the one-loop level. The light-cone formalism provides a potential approach to access these form factors beyond the perturbative regime. However, unlike the covariant formulation, the Poincar\'e symmetry on the light cone is not manifest. In this work, we use perturbation theory as a benchmark to extract the gravitational form factors from the light-front energy-momentum tensor. By comparing results on and off the light cone, we identify T⁺⁺, T⁺ᵃ, T⁺⁻, T¹² as the "good currents" that are properly renormalized and can be used to extract the gravitational form factors.