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  • Open Access

Gauged Q-balls in flat potentials

Julian Heeck* and Yu Zhi†

  • *Contact author: heeck@virginia.edu
  • †Contact author: yz9hy@virginia.edu
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Phys. Rev. D 114, 036011 – Published 10 August, 2026

DOI: https://doi.org/10.1103/pmfb-9mxs

Abstract

Q-balls are large bound-state systems of scalar particles, described classically through localized solutions of the equations of motion. Promoting the required stabilizing U(1) symmetry to a gauge symmetry leads to gauged Q-balls, which cannot grow beyond some maximal size and charge on account of the repulsive gauge interactions. These gauged Q-balls have been studied extensively for scalar potentials that satisfy Coleman’s thin-wall criterion; here, we explore gauged Q-balls in flat potentials, which often occur in supersymmetric models. Even though global Q-balls in flat potentials are qualitatively different from Coleman’s Q-balls, we find that the gauged versions are remarkably similar. We provide analytic approximations for these solitons and compare to numerical solutions. In addition, we study Proca Q-balls, i.e., make the gauge bosons massive, which interpolates between the global and gauged cases.

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Phys. Rev. D 114, 036011– Published 10 August, 2026
  • Received 20 April 2026
  • Accepted 22 July 2026
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