Symplectic gauge theories coupled to matter fields lead to symmetry
enhancement phenomena that have potential applications in such diverse contexts
as composite Higgs, top partial compositeness, strongly interacting dark
matter, and dilaton-Higgs models. These theories are also interesting on
theoretical grounds, for example in reference to the approach to the large-N
limit. A particularly compelling research aim is the determination of the
extent of the conformal window in gauge theories with symplectic groups coupled
to matter, for different groups and for field content consisting of fermions
transforming in different representations. Such determination would have
far-reaching implications, but requires overcoming huge technical challenges.
Numerical studies based on lattice field theory can provide the quantitative
information necessary to this endeavour. We developed new software to implement
symplectic groups in the Monte Carlo algorithms within the Grid framework. In
this paper, we focus most of our attention on the Sp(4) lattice gauge theory
coupled to four (Wilson-Dirac) fermions transforming in the 2-index
antisymmetric representation, as a case study. We discuss an extensive
catalogue of technical tests of the algorithms and present preliminary
measurements to set the stage for future large-scale numerical investigations.
We also include the scan of parameter space of all asymptotically free Sp(4)
lattice gauge theories coupled to varying number of fermions transforming in
the antisymmetric representation.Comment: 41 pages, 16 figure