  A Bose gas subject to a light-induced Rashba spin-orbit coupling possesses a
dispersion minimum on a circle in momentum space; we show that kinematic
constraints due to this dispersion cause interactions to renormalize to
universal, angle-dependent values that govern the phase structure in the
dilute-gas limit. We find that, regardless of microscopic interactions, (a) the
ground state involves condensation at two opposite momenta, and is, in finite
systems, a fragmented condensate; and (b) there is a nonzero-temperature
instability toward the condensation of pairs of bosons. We discuss how our
results can be reconciled with the qualitatively different mean-field phase
diagram, which is appropriate for dense gases.
