Accidental SUSY: Enhanced Bulk Supersymmetry from Brane Back-reaction

TL;DR

This paper demonstrates that bulk supersymmetry can be preserved in 6D supergravity models with branes if a BPS-like relation between brane tension and flux is satisfied, with loop corrections vanishing under these conditions, impacting hierarchy and cosmological constant solutions.

Contribution

It explicitly computes loop effects in 6D gauged supergravity with branes, showing conditions for residual supersymmetry and analyzing its robustness against non-supersymmetric matter.

Findings

Bulk supersymmetry preserved under BPS-like flux-tension relation

Loop corrections to brane curvature vanish in supersymmetric configurations

Residual supersymmetry is robust against certain non-supersymmetric effects

Abstract

We compute how bulk loops renormalize both bulk and brane effective interactions for codimension-two branes in 6D gauged chiral supergravity, as functions of the brane tension and brane-localized flux. We do so by explicitly integrating out hyper- and gauge-multiplets in 6D gauged chiral supergravity compactified to 4D on a flux-stabilized 2D rugby-ball geometry, specializing the results of a companion paper, arXiv:1210.3753, to the supersymmetric case. While the brane back-reaction generically breaks supersymmetry, we show that the bulk supersymmetry can be preserved if the amount of brane-localized flux is related in a specific BPS-like way to the brane tension, and verify that the loop corrections to the brane curvature vanish in this special case. In these systems it is the brane-bulk couplings that fix the size of the extra dimensions, and we show that in some circumstances the bulk geometry dynamically adjusts to ensure the supersymmetric BPS-like condition is automatically satisfied. We investigate the robustness of this residual supersymmetry to loops of non-supersymmetric matter on the branes, and show that supersymmetry-breaking effects can enter only through effective brane-bulk interactions involving at least two derivatives. We comment on the relevance of this calculation to proposed applications of codimension-two 6D models to solutions of the hierarchy and cosmological constant problems.