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arXiv · 2209.12284

$Z_N$-balls: Solitons from $Z_N$-symmetric scalar field theory

F. Buisseret·Y. Brihaye
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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 $N\in\mathbb{N}$ and $N\geq2$, i.e. a potential with a $Z_N$-symmetry. Such configurations are called $Z_N$-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 $Z_N$-balls for $N=$3, 4, 6, 8, 10 and show that only static solutions with zero radial node exist for $N$ odd, while solutions with radial nodes may exist for $N$ even.

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F. Buisseret, Y. Brihaye. 2022-09-29. $Z_N$-balls: Solitons from $Z_N$-symmetric scalar field theory. https://doi.org/10.1103/physrevd.106.105024

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