Breathing mode compactifications and supersymmetry of the brane-world

TL;DR

This work investigates breathing-mode compactifications and their impact on supersymmetry across multiple dimensions: type IIB on S^5 yields a 5D massive supergravity with a well-defined N=2 structure via a detailed reduction of fermionic modes; eleven-dimensional reductions on S^7 and S^4 are analyzed to produce 4D N=2 and 7D N=4 SUSY, respectively, with explicit superpotentials that encode AdS vacua. A central theme is the inclusion of squashing modes, realized through Hopf fibrations over CP^n, which preserves charged fermions and enables consistent truncations to SU(n+1) singlets, thereby achieving controlled N=2 reductions while retaining the breathing mode as a massive multiplet. The results illuminate how brane-world SUSY can be realized in higher-dimensional supergravity contexts and reveal the intricate role of U(1) charges, Killing spinors, and superpotentials in maintaining partial supersymmetry under sphere deformations. These insights advance the understanding of supersymmetric brane-world constructions and their lower-dimensional effective theories, with potential implications for AdS/CFT interpretations and KK-spectrum truncations.

Abstract

It has recently been shown that the Randall-Sundrum brane-world may be obtained from an appropriate doubled D3-brane configuration in type IIB theory. This corresponds, in five dimensions, to a sphere compactification of the original IIB theory with a non-trivial breathing mode supporting the brane. In this paper, we shall study the supersymmetry of this reduction to massive five-dimensional supergravity, and derive the effective supersymmetry transformations for the fermionic superpartners to the breathing mode. We also consider the sphere compactifications of eleven-dimensional supergravity to both four and seven dimensions. For the compactifications on S^5 and S^7, we include a squashing mode scalar and discuss the truncation from N=8 to N=2 supersymmetry.