Supersymmetry and the Brane World

TL;DR

Problem: determine whether gravity localization on a brane can be realized within supersymmetric theories. Approach: analyze first-order BPS flow equations and related warp-factor behavior in $d=5$, $N=2$ gauged supergravity with vector (and tensor) multiplets, including multivalued superpotentials and non-BPS extensions. Findings: in all studied SUSY setups, the warp factor grows away from the wall at AdS critical points (e.g., $H_r=(a'/a)_{oldsymbol{ ext{crit}}}=|W_{ ext{cr}}|>0$), and interpolating walls either fail to localize gravity or produce singular geometries; non-SUSY constructions can mimic RS-like profiles but are not embedded in supersymmetry. Significance: these results delineate the constraints preventing a straightforward SUSY embedding of the brane-world gravity localization mechanism and guide future searches for a consistent SUSY RS-like scenario or a rigorous no-go theorem.

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.