Sp(2N) Lattice Gauge Theories and Extensions of the Standard Model of Particle Physics

We review the current status of the long-term programme of numerical investigation of Sp(2N) gauge theories with and without fermionic matter content. We start by introducing the phenomenological as well as theoretical motivations for this research programme, which are related to composite Higgs models, models of partial top compositeness, dark matter models, and in general to the physics of strongly coupled theories and their approach to the large-N limit. We summarise the results of lattice studies conducted so far in the Sp(2N) Yang-Mills theories, measuring the string tension, the mass spectrum of glueballs and the topological susceptibility, and discuss their large-N extrapolation. We then focus our discussion on Sp(4), and summarise the numerical measurements of mass and decay constant of mesons in the theories with fermion matter in either the fundamental or the antisymmetric representation, first in the quenched approximation, and then with dynamical fermions. We finally discuss the case of dynamical fermions in mixed representations, and exotic composite fermion states such as the chimera baryons. We conclude by sketching the future stages of the programme. We also describe our approach to open access.

Automated summary

This article reviews the current status of the long-term numerical investigation programme of Sp(2N) gauge theories with and without fermionic matter content. The motivations for this research programme, related to composite Higgs models, partial top compositeness models, dark matter models, and strongly coupled theories, are introduced. The results of lattice studies in the Sp(2N) Yang-Mills theories, including the measurements of string tension, mass spectrum of glueballs, and topological susceptibility, are summarized. The measurements of mass and decay constant of mesons in the Sp(4) theories with fermion matter in different representations are discussed, along with the case of dynamical fermions in mixed representations and exotic composite fermion states.