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In this article we summarize our efforts in simulating Yang-Mills theoriescoupled to matter fields transforming under the fundamental and adjointrepresentations of the gauge group. In the context of composite Higgsscenarios, gauge theories with mixed representation fields have been suggestedto describe the fundamental interactions well beyond the electroweakunification scale, and they are also closely related to supersymmetric QCD. Inaddition, they are studied as deformations of theories with pure adjoint matterin the context of adiabatic continuity. We provide some first results for bareparameter tuning and interdependence of the two representations. We alsoinvestigate how the chiral symmetry breaking or a conformal scenario can berealized and checked in such theories.

Lattice simulations of a gauge theory with mixed adjoint-fundamental matter