Symplectic lattice gauge theories on Grid: approaching the conformal window

TL;DR

This paper develops new lattice simulation software to study symplectic gauge theories, aiming to determine the conformal window and explore their applications in particle physics and beyond.

Contribution

The authors created specialized software for simulating symplectic groups on the lattice and conducted preliminary studies on Sp(4) gauge theory with fermions, advancing the investigation of conformal windows.

Findings

Developed algorithms for symplectic groups in lattice simulations.

Performed preliminary measurements on Sp(4) with antisymmetric fermions.

Mapped parameter space of Sp(4) gauge theories with various fermion counts.

Abstract

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.