Supersymmetry and the Brane World

TL;DR

This paper examines whether gravity can be localized on a brane within supersymmetric theories and concludes that, despite various approaches, such localization remains unachieved in these models.

Contribution

The study provides a comprehensive analysis of supersymmetric flow equations in gauged supergravity, demonstrating the inherent difficulties in achieving gravity localization on branes.

Findings

Gravity localization does not occur in supersymmetric gauged supergravity models.

Including tensor multiplets does not change the outcome.

Recent attempts at BPS brane-worlds also fail to achieve localization.

Abstract

We investigate the possibility of gravity localization on the brane in the context of supersymmetric theories. To realize this scenario one needs to find a theory with the supersymmetric flow stable in IR at two critical points, one with positive and the other with negative values of the superpotential. We perform a general study of the supersymmetric flow equations of gauged massless supergravity interacting with arbitrary number of vector multiplets and demonstrate that localization of gravity does not occur. The same conclusion remains true when tensor multiplets are included. We analyze all recent attempts to find a BPS brane-world and conclude that localization of gravity on the brane in supersymmetric theories remains a challenging but unsolved problem.