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

TL;DR

This paper employs the Wilson flow to renormalize the energy-momentum tensor in a 3D $SU(N)$ scalar field theory, enabling predictions of cosmological observables in holographic models.

Contribution

It introduces a lattice-based renormalization method for the EMT using Wilson flow in a 3D $SU(N)$ scalar theory, with numerical results for $N=2$.

Findings

Numerical determination of the EMT mixing coefficient for $N=2$.

Successful application of Wilson flow for lattice renormalization of EMT.

Foundation for predicting CMB spectra from non-perturbative QFT regimes.

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 $\phi^4$ interaction. On the lattice, the energy-momentum tensor (EMT) in this theory can mix with the operator $\phi^2$. 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.