If quark matter is energetically favored over nuclear matter at zero temperature and pressure, then it has long been expected to take the form of strange quark matter (SQM), with comparable amounts of $u$, $d$, and $s$ quarks. The possibility of quark matter with only $u$ and $d$ quarks ($ud\mathrm{QM}$) is usually dismissed because of the observed stability of ordinary nuclei. However, we find that $ud\mathrm{QM}$ generally has lower bulk energy per baryon than normal nuclei and SQM. This emerges in a phenomenological model that describes the spectra of the lightest pseudoscalar and scalar meson nonets. Taking into account the finite size effects, $ud\mathrm{QM}$ can be the ground state of baryonic matter only for baryon number $A>A_{\min }$ with $A_{\min }\gtrsim 300$. This ensures the stability of ordinary nuclei and points to a new form of stable matter just beyond the periodic table.

We study the gravitational-wave signal stemming from strongly coupled models featuring both, dark chiral and confinement phase transitions. We therefore identify strongly coupled theories that can feature a first-order phase transition. Employing the Polyakov-Nambu-Jona-Lasinio model, we focus our attention on SU(3) Yang-Mills theories featuring fermions in fundamental, adjoint, and two-index symmetric representations. We discover that for the gravitational-wave signals analysis, there are significant differences between the various representations. Interestingly we also observe that the two-index symmetric representation leads to the strongest first-order phase transition and therefore to a higher chance of being detected by the Big Bang Observer experiment. Our study of the confinement and chiral phase transitions is further applicable to extensions of the Standard Model featuring composite dynamics.

We investigate interacting quark matter (IQM), including the perturbative QCD correction and color superconductivity, for both up-down quark matter and strange quark matter. We first derive an equation of state (EOS) unifying all cases by a simple reparametrization and rescaling, through which we manage to maximally reduce the number of degrees of freedom. We find, in contrast to the conventional EOS $p=1/3(\rho -4B_{\mathrm{eff}})$ for noninteracting quark matter, that taking the extreme strongly interacting limit on the unified IQM EOS gives $p=\rho -2B_{\mathrm{eff}}$, where $B_{\mathrm{eff}}$ is the effective bag constant. We employ the unified EOS to explore the properties of pure interacting quark stars (IQSs) composed of IQM. We describe how recent astrophysical observations, such as the pulsar-mass measurements, the NICER analysis, and the binary merger gravitational-wave events GW170817, GW190425, and GW190814, further constrain the parameter space. An upper bound for the maximum allowed mass of IQSs is found to be $M_{\mathrm{TOV}}\lesssim 3.23M_{\odot }$. Our analysis indicates a new possibility that the currently observed compact stars, including the recently reported GW190814’s secondary component ($M=2.59_{-0.09}^{+0.08}{M}_{\odot }$), can be quark stars composed of interacting quark matter.

We determine, for the first time, the scaling dimensions of a family of fixed-charge operators stemming from the critical $O(N)$ model in $4-\epsilon$ dimensions to the leading and next to leading order terms in the charge expansion but to all orders in the coupling. We test our results to the maximum known order in perturbation theory while determining higher order terms.

We consider possible extensions of the standard model that are not only completely asymptotically free, but are such that the UV fixed point is completely UV attractive. All couplings flow towards a set of fixed ratios in the UV. Motivated by low scale unification, semi-simple gauge groups with elementary scalars in various representations are explored. The simplest model is a version of the Pati-Salam model. The Higgs boson is truly elementary but dynamical symmetry breaking from strong interactions may be needed at the unification scale. A hierarchy problem, much reduced from grand unified theories, is still in need of a solution.