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.
Normal modes in thermal AdS via the Selberg zeta function
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abstract
The heat kernel and quasinormal mode methods of computing 1-loop partition functions of spin $s$ fields on hyperbolic quotient spacetimes $\mathbb{H}^{3}/\mathbb{Z}$ are related via the Selberg zeta function. We extend that analysis to thermal $\text{AdS}_{2n+1}$ backgrounds, with quotient structure $\mathbb{H}^{2n+1}/\mathbb{Z}$. Specifically, we demonstrate the zeros of the Selberg function encode the normal mode frequencies of spin fields upon removal of non-square-integrable modes. With this information we construct the 1-loop partition functions for symmetric transverse traceless tensors in terms of the Selberg zeta function and find exact agreement with the heat kernel method.
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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.