Q-balls are stable, compact objects (more precisely, nontopological solitons) that can arise in complex scalar field theories with a U(1) symmetry in which the potential adheres to certain criteria. These objects are of phenomenological interest as candidates for macroscopic dark matter, an as of yet still relatively underconstrained region of dark matter parameter space. Many of the features of Q-balls -- including their size, charge, energy, and stability dynamics -- can be qualitatively and approximately quantitatively extracted from their potential under minimal assumptions, although exact solutions are only attainable numerically. A thorough analytic study of Q-balls leads to a simplified understanding of the interconnectedness of their parameters, attributes, and dynamics, culminating most notably in a direct mapping between global Q-ball parameters and related gauged and Proca Q-ball parameters.
This work presents several novel results, as previously published by the author and collaborators, including: precise analytic profiles for global, gauged, and Proca Q-balls; proof of various Q-ball relations and identities; precise analytic estimates of a Q-ball's radius, charge, and energy in terms of a universal Q-ball parameter; new bounds on Q-ball radii and stability; and the aforementioned parameter mapping between global Q-balls and gauged and Proca Q-balls. More complex Q-solitons, including excited Q-balls and Q-shells, are also discussed. Together, these objects represent a new candidate class for dark matter.