AdS_{d+1} --> AdS_d

TL;DR

This paper constructs an SO(2,d) invariant AdS generalization of the Nambu-Goto action using coset methods, describing the dynamics of a Nambu-Goldstone scalar from symmetry breaking in AdS spaces.

Contribution

It introduces a new AdS invariant scalar action and its vector field equivalent, derived via coset methods for symmetry breaking from AdS_{d+1} to AdS_d.

Findings

Derived the scalar action with SO(2,d) invariance

Established the vector field theory equivalent

Provided a geometric interpretation of the symmetry breaking

Abstract

Coset methods are used to construct the action describing the dynamics of the (massive) Nambu-Goldstone scalar degree of freedom associated with the spontaneous breaking of the isometry group of AdS_{d+1} space to that of an AdS_d subspace. The resulting action is an SO(2,d) invariant AdS generalization of the Nambu-Goto action. The vector field theory equivalent action is also determined.