Baryonic Q-balls as Dark Matter

Supersymmetric extensions of the Standard Model predict the existence of Q-balls, some of which can be entirely stable. Affleck–Dine baryogenesis can result in a copious production of stable baryonic Q-balls, which can presently exist as a form of dark matter. 1 Q-balls from Supersymmetry In a class of theories with interacting scalar fields φ that carry some conserved global charge, the ground state is a Q-ball [1,2], a lump of coherent scalar condensate that can be described semiclassically as a non-topological soliton of the form φ(x, t) = eφ̄(x). (1) Q-balls exist whenever the scalar potential satisfies certain conditions that were first derived for a single scalar degree of freedom [1] with some abelian global charge and were later generalized to a theory of many scalar fields with different charges [3]. Non-abelian global symmetries [4] and abelian local symmetries [5] can also yield Q-balls. For a simple example, let us consider a field theory with a scalar potential U(φ) that has a global minimum U(0) = 0 at φ = 0. Let U(φ) have an unbroken global U(1) symmetry at the origin, φ = 0. And let the scalar field φ have a unit charge with respect to this U(1). The charge of some field configuration φ(x, t) is