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The Hosotani mechanism claims to achieve gauge-symmetry breaking, forinstance $SU(3) \to SU(2)\times U(1)$. To verify this claim, we propose tomonitor the stability of a topological defect stable under a gauge subgroup butnot under the whole gauge group, like a $U(1)$ flux state or monopole in thecase above. We use gauge invariant operators to probe the presence of thetopological defect to avoid any ambiguity introduced by gauge fixing. Ourmethod also applies to an ordinary gauge-Higgs system.

Gauge-invariant signatures of spontaneous gauge symmetry breaking by the Hosotani mechanism