Dynamics of (SUSY) AdS Space Isometry Breaking

TL;DR

This paper explores the dynamics and stability of Nambu-Goldstone modes resulting from spontaneous symmetry breaking in AdS spaces and SUSY AdS spaces, revealing instability in certain dilatonic modes and deriving a gravity action with a massive vector field.

Contribution

It presents the actions for Nambu-Goldstone modes from symmetry breaking in AdS and SUSY AdS spaces, including the analysis of stability and the derivation of a modified Einstein-Hilbert action.

Findings

Dilatonic Nambu-Goldstone mode is unstable in the SUSY AdS case.

No instability found in other symmetry breaking scenarios.

Gauging symmetries yields an Einstein-Hilbert action with a massive Abelian vector field.

Abstract

Actions governing the dynamics of the Nambu-Goldstone modes resulting from the spontaneous breaking of the SO(4,2) and $SU(2,2|1)$ isometries of five dimensional anti-de Sitter space ($AdS_{5}$) and SUSY $AdS_{5}\times S_1$ spaces respectively due to a restriction of the motion to embedded four dimensional $AdS_{4}$ space and four dimensional Minkowski space ($M_4$) probe branes are presented. The dilatonic Nambu-Goldstone mode governing the motion of the $M_4$ space probe brane into the covolume of the SUSY $AdS_5\times S_1$ space is found to be unstable. No such instablility appears in the other cases. Gauging these symmetries leads to an Einstein-Hilbert action containing, in addition to the gravitational vierbein, a massive Abelian vector field coupled to gravity.