Sp(4) gauge theories and beyond the standard model physics

We review numerical results for models with gauge group Sp(2N), discussing the glueball spectrum in the large-N limit, the quenched meson spectrum of Sp(4) with Dirac fermions in the fundamental and in the antisymmetric representation and the Sp(4) gauge model with two dynamical Dirac flavours. We also present preliminary results for the meson spectrum in the Sp(4) gauge theory with two fundamental and three antisymmetric Dirac flavours. The main motivation of our programme is to test whether this latter model is viable as a realisation of Higgs compositeness via the pseudo Nambu Goldstone mechanism and at the same time can provide partial top compositeness. In this respect, we report and briefly discuss preliminary results for the mass of the composite baryon made with two fundamental and one antisymmetric fermion (chimera baryon), whose physical properties are highly constrained if partial top compositeness is at work. Our investigation shows that a fully non-perturbative study of Higgs compositeness and partial top compositeness in Sp(4) is within reach with our current lattice methodology.

Quenched glueball spectrum from functional equations

We give an overview of results for the quenched glueball spectrum from two-body bound state equations based on the 3PI effective action. The setup, which uses self-consistently calculated two- and three-point functions as input, is completely self-contained and does not have any free parameters except for the coupling. The results for JPC = 0±+, 2±+, 3±+, 4±+ are in good agreement with recent lattice results where available. For the pseudoscalar glueball, we present first results from a two-loop complete calculation, rendering also the bound state calculation fully self-consistent.

Confinement and Pseudoscalar Glueball Spectrum in the 2 + 1D QCD-Like Theory from the Non-Susy D2 Brane

We study two important properties of 2+1D QCD, namely confinement and Pseudoscalar glueball spectrum, using holographic approach. The confined state of the bounded quark-antiquark pair occurs in the self-coupling dominated nonperturbative regime, where the free gluons form the bound states, known as glueballs. The gauge theory corresponding to low energy decoupled geometry of isotropic non-supersymmetric D2 brane, which is again similar to the 2+1D YM theory, has been taken into account but in this case the coupling constant is found to vary with the energy scale. At BPS limit, this theory reduces to supersymmetric YM theory. We have considered NG action of a test string and calculate the potential of such confined state located on the boundary. The QCD flux tube tension for large quark-antiquark separation is observed to be a monotonically increasing function of running coupling. The mass spectrum of Pseudoscalar glueball is evaluated numerically from the fluctuations of the axion in the gravity theory using WKB approximation. This produces the mass to be related to the string tension and the levels of the first three energy states. The various results that we obtained quite match with those previously studied through the lattice approach.

SU(N) gauge theories in 3+1 dimensions: glueball spectrum, string tensions and topology

We calculate the low-lying glueball spectrum, several string tensions and some properties of topology and the running coupling for SU(N) lattice gauge theories in 3 + 1 dimensions. We do so for 2 ≤ N ≤ 12, using lattice simulations with the Wilson plaquette action, and for glueball states in all the representations of the cubic rotation group, for both values of parity and charge conjugation. We extrapolate these results to the continuum limit of each theory and then to N = ∞. For a number of these states we are able to identify their continuum spins with very little ambiguity. We calculate the fundamental string tension and k = 2 string tension and investigate the N dependence of the ratio. Using the string tension as the scale, we calculate the running of a lattice coupling and confirm that g2(a) ∝ 1/N for constant physics as N → ∞. We fit our calculated values of a√σ with the 3-loop β-function, and extract a value for $$ {\Lambda}_{\overline{MS}} $$ Λ MS ¯ , in units of the string tension, for all our values of N, including SU(3). We use these fits to provide analytic formulae for estimating the string tension at a given lattice coupling. We calculate the topological charge Q for N ≤ 6 where it fluctuates sufficiently for a plausible estimate of the continuum topological susceptibility. We also calculate the renormalisation of the lattice topological charge, ZQ(β), for all our SU(N) gauge theories, using a standard definition of the charge, and we provide interpolating formulae, which may be useful in estimating the renormalisation of the lattice θ parameter. We provide quantitative results for how the topological charge ‘freezes’ with decreasing lattice spacing and with increasing N. Although we are able to show that within our typical errors our glueball and string tension results are insensitive to the freezing of Q at larger N and β, we choose to perform our calculations with a typical distribution of Q imposed upon the fields so as to further reduce any potential systematic errors.

Higher spin glueballs from functional methods

We calculate the glueball spectrum for spin up to $$J=$$ J = 4 and positive charge parity in pure Yang–Mills theory. We construct the full bases for $$J=$$ J = 0, 1, 2, 3, 4 and discuss the relation to gauge invariant operators. Using a fully self-contained truncation of Dyson–Schwinger equations as input, we obtain ground states and first and second excited states from extrapolations of the eigenvalue curves. Where available, we find good quantitative agreement with lattice results

Non-perturbative aspects of Sp(2N) gauge theories

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.

The glueball spectrum of SU(3) gauge theory in 3 + 1 dimensions

We calculate the low-lying glueball spectrum of the SU(3) lattice gauge theory in 3 + 1 dimensions for the range β ≤ 6.50 using the standard plaquette action. We do so for states in all the representations R of the cubic rotation group, and for both values of parity P and charge conjugation C . We extrapolate these results to the continuum limit of the theory using the confining string tension σ as our energy scale. We also present our results in units of the r0 scale and, from that, in terms of physical ‘GeV’ units. For a number of these states we are able to identify their continuum spins J with very little ambiguity. We also calculate the topological charge Q of the lattice gauge fields so as to show that we have sufficient ergodicity throughout our range of β, and we calculate the multiplicative renormalisation of Q as a function of β. We also obtain the continuum limit of the SU(3) topological susceptibility.