For large gauge coupling, SU(N) Ginzburg-Landau models with N > 2 show two phase transitions, with an intermediate CP^{N-1}-neutral phase that has composite order, no Meissner effect, and no O(M) description.
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Vortices and composite order in $\mathrm{SU}(N)$ theories coupled to Abelian gauge field
For large gauge coupling, SU(N) Ginzburg-Landau models with N > 2 show two phase transitions, with an intermediate CP^{N-1}-neutral phase that has composite order, no Meissner effect, and no O(M) description.