The holographic principle allows us to study the physics of the early universe in terms of three-dimensional boundary quantum field theories. For instance, the power spectrum of the CMB at high multipoles has in this way been post-dicted successfully in terms of calculations for 2pt functions of the energy-momentum tensor (EMT) in perturbation theory. The lower end of the power spectrum maps onto dynamics non-perturbative in nature and are therefore best predicted by lattice simulations.
Here we study massless SU(N) scalar matrix field theory on the lattice as a first candidate theory. We present a comprehensive study of its critical properties in terms of a finite-size-scaling study and its large-N scaling both numerically and analytically.
In a next step we compute 2pt functions of the EMT in this theory which will allow us to make first lattice-based predictions for the spectrum of the CMB at low multipoles. Results for the EMT 2pt function and its renormalisation are discussed in the talk by Joseph Lee.