UC Merced

This thesis includes two parts discussing two fascinating areas of fundamental physics. \textbf{Part (I)} explores the enigma of quark confinement within the intricate domain of quantum field theory, addressing a foundational puzzle in particle physics. Quark confinement dictates that quarks are bound within hadrons, so we cannot observe quarks as free, isolated particles. Despite extensive efforts over the past fifty years, the theoretical foundation of quark confinement in quantum chromodynamics (QCD) is still unclear. Studying the Schwinger effect (particle-antiparticle pair creation in vacuum in the presence of a strong external electromagnetic field) can pave the way to explore the behavior of quarks within hadrons. We utilize an indirect method, in particular the so-called AdS/QCD correspondence, to investigate the response of a QCD-like gauge theory to a static electromagnetic field. AdS/QCD correspondence is a form of gauge/gravity duality. This duality connects a gauge theory (representing particle physics) to a gravitational theory (specifically, string theory with an Anti-de Sitter background metric). Leveraging this method enables us to study the Schwinger effect for quark-antiquark pairs through potential analysis and calculation of the pair-production rate $\Gamma$. Our findings show that both the potential analysis and the calculation of the pair-production rate yield consistent results. We identify two critical electric fields $E_{s}$ and $E_{c}$ as lower and upper bounds of a range in which pair production can occur only by tunneling through a potential barrier. Below $E_{s}$, the potential barrier is insurmountable, and pair production cannot happen. Above $E_{c}$, there is no potential barrier to restrict the pair production. While previous studies have explored various aspects of the Schwinger effect using AdS/QCD duality, further investigation is required for scenarios involving QCD-like gauge theories with simultaneous electric and magnetic fields. Addressing this research gap, our findings reveal that a magnetic field perpendicular to the electric field suppresses $\Gamma$ and increases $E_{s}$. Conversely, a purely parallel magnetic field does not influence the system's response to an external electric field but enhances $\Gamma$ in the presence of a perpendicular magnetic field. \textbf{Part (II)} ventures into the cosmos, examining the formation of young stellar groups (both bound star clusters and unbound stellar associations) within a full cosmological context. A young stellar group is a collection of newly born stars moving together as a relatively coherent unit through a galaxy. Recent observational advancements, driven by improved precision of Gaia DR3, along with complementary near-field studies like PHANGS-HST and PHANGS-JWST, have significantly enhanced our understanding of stellar groups in the Milky Way and local universe galaxies, enabling us to study the conditions and environment that set clustered star formation across a statistically significant sample. Yet despite the exciting progress in observations, there is still a notable absence of robust theoretical cosmological models to interpret the data. Recent advancements in generating galaxy zoom-in simulations enable the comprehensive study of the formation and evolution of giant molecular clouds and stellar groups within a cosmological galactic framework and, in turn, facilitate filling the gap between observations and theoretical models. We present the fundamental properties of young massive stellar groups, both bound and unbound, formed within or near the galactic disk at the present time (at redshifts $z < 0.008$) in the \Latte suite of FIRE-2 Milky Way-like galaxy simulations. Our analysis encompasses the measurement of various characteristics for each stellar group, including its boundedness, mass, size (stellar group’s radius), 1D velocity dispersion, dispersion in age, and dispersion in metallicity [Fe/H]. We find the properties of simulated stellar groups with ages between 0 and 3 million years are within the range of values reported in observational studies. Our results depict the capability of \Latte simulations to generate reasonably realistic star clusters and associations and set the stage for the forthcoming project that will focus on generating synthetic images of the simulated stellar groups and measuring their properties by utilizing the conventional pipelines used in observational studies. This approach will allow a more consistent comparison between simulations and observations, aiding in the establishment of benchmarks for interpreting observations and advancing our understanding of various aspects of galaxy formation, such as stellar evolution, the impact of feedback on galactic dynamics, and the processes involved in star and planetary system formation.