Renormalization of the $3D$ $SU(N)$ scalar energy-momentum tensor using the Wilson flow

Abstract

In the holographic approach to cosmology, cosmological observables are described in terms of correlators of a three-dimensional boundary quantum field theory. As a concrete model, we study the 3D massless SU(N) scalar matrix field theory with a 𝜙 4 interaction. On the lattice, the energymomentum tensor (EMT) in this theory can mix with the operator 𝜙 2 . We utilize the Wilson Flow to renormalize the EMT on the lattice, and present numerical results for the mixing coefficient for 𝑁 = 2. Obtaining the renormalized EMT will allow us to make predictions for the CMB power spectra in the regime where the dual QFT is non-perturbative.