Spinning Q-balls -: art. no. 085003

We present numerical evidence for the existence of spinning generalizations for nontopological Q-ball solitons in the theory of a complex scalar field with a nonrenormalizable self-interaction. To the best of our knowledge, this provides the first explicit example of spinning solitons in (3+1)-dimensional Minkowski space. In addition, we find an infinite discrete family of radial excitations of nonrotating Q-balls, and construct also spinning Q-balls in 2+1 dimensions.