Nonlinear realization of local symmetries of AdS space

TL;DR

This paper develops a coset-based method to construct an AdS-invariant action describing the dynamics of a brane in AdS space, revealing a massive vector field coupled to gravity on the brane.

Contribution

It introduces a novel coset construction for the spontaneous breaking of local AdS symmetries and derives an invariant action including a massive vector field.

Findings

The action is SO(2,d) invariant and resembles the Einstein-Hilbert form.

Includes a massive vector field localized on the brane.

Long wavelength limit matches a massive vector coupled to AdS gravity.

Abstract

Coset methods are used to construct the action describing the dynamics associated with the spontaneous breaking of the local symmetries of AdS_{d+1} space due to the embedding of an AdS_d brane. The resulting action is an SO(2,d) invariant AdS form of the Einstein-Hilbert action, which in addition to the AdS_d gravitational vielbein, also includes a massive vector field localized on the brane. Its long wavelength dynamics is the same as a massive Abelian vector field coupled to gravity in AdS_d space.