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Coupled boundary and bulk fields in anti-de Sitter

Kazuya Koyama·Andrew Mennim·David Wands
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Abstract

We investigate the dynamics of a boundary field coupled to a bulk field with a linear coupling in an anti-de Sitter bulk spacetime bounded by a Minkowski (Randall-Sundrum) brane. An instability criterion for the coupled boundary and bulk system is found. There exists a tachyonic bound state when the coupling is above a critical value, determined by the masses of the brane and bulk fields and AdS curvature scale. This bound state is normalizable and localised near the brane, and leads to a tachonic instability of the system on large scales. Below the critical coupling, there is no tachyonic state and no bound state. Instead, we find quasi-normal modes which describe stable oscillations, but with a finite decay time. Only if the coupling is tuned to the critical value does there exist a massless stable bound state, as in the case of zero coupling for massless fields. We discuss the relation to gravitational perturbations in the Randall-Sundrum brane-world.

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Kazuya Koyama, Andrew Mennim, David Wands. 2005-04-25. Coupled boundary and bulk fields in anti-de Sitter. https://doi.org/10.1103/physrevd.72.064001

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