Critical behaviour and phase structure of 3d Scalar+Gauge Field Theories in the adjoint representation

In a class of holographic models for cosmology, the dual theory is given by a massless super-renormalisable QFT in 3 dimensions. In order to obtain cosmological observables, correlators of this QFT may be obtained via lattice field theory. Previous work has focused on scalar $\phi^4$ matrix theories in the adjoint representation of SU(N). In this work we present preliminary results in the critical behaviour and phase structure of the theory with an SU(N) scalar field coupled to gauge fields by utilising the Heatbath-Overrelaxation (HBOR) algorithm in lattice field theory.