Nonlinear Realization of Supersymmetric AdS Space Isometries

TL;DR

This paper explores how supersymmetric and non-supersymmetric $AdS_5$ space isometries are realized on Minkowski space, constructing effective actions with Nambu-Goldstone modes and analyzing stability properties.

Contribution

It presents a nonlinear realization framework for supersymmetric $AdS_5$ isometries and derives effective actions, highlighting the instability of the dilatonic mode in the supersymmetric case.

Findings

Dilatonic mode is unstable in supersymmetric case.

Bulk $AdS_5$ cannot sustain the Minkowski probe brane in supersymmetric scenario.

No instability observed in the non-supersymmetric case.

Abstract

The isometries of $AdS_5$ space and supersymmetric $AdS_5\otimes S_1$ space are nonlinearly realized on four dimensional Minkowski space. The resultant effective actions in terms of the Nambu-Goldstone modes are constructed. The dilatonic mode governing the motion of the Minkowski space probe brane into the covolume of supersymmetric $AdS_5$ space is found to be unstable and the bulk of the $AdS_5$ space is unable to sustain the brane. No such instablility appears in the non-supersymmetric case.