The missing top of AdS resonance structure

TL;DR

This paper proves that for a massless scalar field in AdS with certain nonlinear couplings, the most efficient energy transfer channels are absent when the product of the coupling power and dimension is even, revealing new conservation laws.

Contribution

It demonstrates the absence of key resonant channels in AdS scalar fields with nonlinear couplings when Nd is even, extending understanding beyond spherical symmetry.

Findings

No energy transfer for N=3 in the studied system.

Half of the resonant channels are suppressed for N=4, leading to additional conservation laws.

Resonant energy transfer mechanisms are constrained by the parity of Nd.

Abstract

We study a massless scalar field in AdS_{d+1} with a nonlinear coupling \phi^N and not limited to spherical symmetry. The free-field-eigenstate spectrum is strongly resonant, and it is commonly believed that the nonlinear coupling leads to energy transfer between eigenstates. We prove that when $Nd$ is even, the most efficient resonant channels to transfer energy are always absent. In particular, for N=3 this means no energy transfer at all. For N=4, this effectively kills half of the channels, leading to the same set of extra conservation laws recently derived for gravitational interactions within spherical symmetry.