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We study two different SU(2) gauge-scalar theories in 3 and 4 spacetimedimensions. Firstly, we focus on the 3 dimensional SU(2) theory with multipleHiggs fields in the adjoint representation, that can be mapped to cupratesystems in condensed matter physics which host a rich phase diagram includinghigh-Tc superconductivity. It has been proposed that the theory with 4 adjointHiggs fields can be used to explain the physics of hole-doped cuprates for awide range of parameters. We show exploratory results on the phase diagram ofthe theory.  On the other hand, we are interested in the 4 dimensional theory with 2 setsof fundamental scalar (Higgs) fields, which is relevant to the 2 Higgs DoubletModel (2HDM), a proposed extension to the Standard Model of particle physics.The goal is to understand the particle spectrum of the theory at zerotemperature and the electroweak phase transition at finite temperature. Wepresent exploratory results on scale setting and the multi-parameter phasediagram of this theory.

Study of SU(2) gauge theories with multiple Higgs fields in different representations