We study two different SU(2) gauge-scalar theories in 3 and 4 spacetime
dimensions. Firstly, we focus on the 4 dimensional theory with 2 sets of
fundamental scalar (Higgs) fields, which is relevant to the 2 Higgs Doublet Model
(2HDM), a proposed extension to the Standard Model of particle physics.
The goal is to understand the particle spectrum of the theory at zero temperature
and the electroweak phase transition at finite temperature. We present exploratory
results on scale setting and the multi-parameter phase diagram of this theory.
On the other hand, we are interested in the 3 dimensional SU(2) theory with
multiple Higgs fields in the adjoint representation, that can be mapped to cuprate
systems in condensed matter physics which host a rich phase diagram including
high-Tc superconductivity. It has been proposed that the theory with 4 adjoint Higgs
fields can be used to explain the physics of hole-doped cuprates for a wide range
of parameters while the theory with 1 real adjoint Higgs field would describe the
physics of electron-doped cuprates. We show exploratory results on the phase
diagram of these theories.