Neumann-boundary scalars in AdS_{2..5} get one-loop phase diagrams that are much more restricted than the Dirichlet ones, and symmetry breaking is often blocked by unitarity and thermal-series convergence constraints.
Harmonic analysis and propagators on homogeneous spaces,
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Neumann scalars in AdS: partition functions and phases
Neumann-boundary scalars in AdS_{2..5} get one-loop phase diagrams that are much more restricted than the Dirichlet ones, and symmetry breaking is often blocked by unitarity and thermal-series convergence constraints.