TL;DR
This paper derives the action for a co-dimension one brane in AdS space under the Carroll limit, revealing its symmetry properties and dual descriptions, with potential implications for holography and spacetime symmetries.
Contribution
It introduces a coset-based method to construct the brane action in AdS-Carroll spacetime, highlighting non-linear symmetries and dualities in this limit.
Findings
The brane action is invariant under AdS-Carroll symmetries.
The Nambu-Goldstone field shows a static spatial profile with time-dependent momentum.
A dual AdS-C vector field theory is derived.
Abstract
Coset methods are used to determine the action of a co-dimension one brane (domain wall) embedded in (d+1)-dimensional AdS space in the Carroll limit in which the speed of light goes to zero. The action is invariant under the non-linearly realized symmetries of the AdS-Carroll spacetime. The Nambu-Goldstone field exhibits a static spatial distribution for the brane with a time varying momentum density related to the brane's spatial shape as well as the AdS-C geometry. The AdS-C vector field dual theory is obtained.
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