Renormalization of the energy-momentum tensor in three-dimensional scalar SU(N) theories using the Wilson flow

A nonperturbative determination of the energy-momentum tensor is essential for understanding the physics of strongly coupled systems. The ability of the Wilson flow to eliminate divergent contact terms makes it a practical method for renormalizing the energy-momentum tensor on the lattice. In this paper, we utilize the Wilson flow to define a procedure to renormalize the energy-momentum tensor for a three-dimensional massless scalar field in the adjoint of SU(N) with a φ4 interaction on the lattice. In this theory the energy-momentum tensor can mix with φ2 and we present numerical results for the mixing coefficient for the N = 2 theory.