Non-perturbative aspects of Sp(2N) gauge theories - JACK HOLLIGAN (2021)
Yang-Mills theories based on the symplectic groups – denoted by Sp(2N) – are inter-esting for both theoretical and phenomenological reasons. Sp(2N) theories with two fundamental Dirac fermions give rise to pseudo-Nambu-Goldstone bosons which can be interpreted as a composite Higgs particle. This framework can describe the existing Higgs boson without the need for unnatural ﬁne-tuning. This justiﬁes a programme of wider investigations of Sp(2N) gauge theories aimed at understanding their general behaviour. In this work, we study the glueball mass spectrum for Sp(2N) Yang-Mills theories using the variational method applied to Monte-Carlo generated gauge conﬁg-urations. This is carried out both for ﬁnite N and in the limit N → ∞. The results are compared to existing results for SU(N) Yang-Mills theories, again, for ﬁnite- and large-N. Our glueball analysis is then used to investigate some conjectures related to the behaviour of the spectrum in Yang-Mills theories based on a generic non-Abeliangauge group G. We also ﬁnd numerical evidence that Sp(2N) groups conﬁne both for ﬁnite and large N. As well as studying the glueball spectrum, we examine the quenched-meson spectrum for fermions in the fundamental, antisymmetric and sym-metric representations for N = 2 and N = 3. This study enables us to provide a ﬁrst account of how the related observables vary with N. The investigations presented in this work contribute to our understanding of the non-perturbative dynamics of Sp(2N) gauge theories in connection with Higgs compositeness and, more in general, with fun-damental open problems in non-Abelian gauge theories such as conﬁnement and global symmetry breaking.