ZN-balls: Solitons from ZN-symmetric scalar field theory

Abstract

We discuss the conditions under which static, finite-energy, configurations of a complex scalar field ϕ with constant phase and spherically-symmetric norm exist in a potential of the form V(ϕ*ϕ, ϕ^N, ϕ^*N) with N ∈ N and N ≥ 2, i.e., a potential with a ZN-symmetry. Such configurations are called ZN-balls. We build explicit solutions in (3 + 1)-dimensions from a model mimicking effective field theories based on the Polyakov loop in finite-temperature SU(N) Yang-Mills theory. We find ZN-balls for N = 3, 4, 6, 8, 10, and show that only static solutions with zero radial nodes exist for N odd, while solutions with radial nodes may exist for N even.