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A nonperturbative determination of the energy-momentum tensor is essentialfor understanding the physics of strongly coupled systems. The ability of theWilson flow to eliminate divergent contact terms makes it a practical methodfor renormalizing the energy-momentum tensor on the lattice. In this paper, weutilize the Wilson flow to define a procedure to renormalize theenergy-momentum tensor for a three-dimensional massless scalar field in theadjoint of $SU(N)$ with a $\varphi^4$ interaction on the lattice. In thistheory the energy-momentum tensor can mix with $\varphi^2$ and we presentnumerical results for the mixing coefficient for the $N=2$ theory.

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