Progress in $Sp(2N)$ lattice gauge theories

TL;DR

This paper reviews recent progress in lattice studies of $Sp(2N)$ gauge theories, including mass spectra and topological properties, with implications for composite Higgs and dark matter models.

Contribution

It presents new lattice results on the glueball spectrum, topology, and meson masses in $Sp(2N)$ theories, especially for $Sp(4)$ with dynamical fermions, advancing understanding of these gauge theories.

Findings

Glueball mass spectrum characterized for $Sp(2N)$ theories.

Topological properties of pure $Sp(2N)$ gauge theories analyzed.

Meson spectra obtained with dynamical fermions in $Sp(4)$.

Abstract

Lattice studies of gauge theories with symplectic gauge groups provide valuable information about gauge dynamics, and complement the results of lattice investigations focused on unitary gauge groups. These theories play a central role in phenomenological contexts such as composite Higgs and strongly interacting dark matter models. We report on recent progress of our lattice research programme, starting from the glueball mass spectrum and the topology of the pure gauge theory. We present our results on the mass spectrum of mesons in the quenched approximation, by varying the number of colours in the symplectic group. For the $Sp(4)$ theory, we focus on results obtained with dynamical fermion matter content comprising both fundamental and 2-index antisymmetric representations of the gauge group, as dictated by a well known model of composite Higgs with partial top compositeness.