Supersymmetry in Singular Spaces

TL;DR

This paper develops a framework for implementing supersymmetry in singular spaces, enabling consistent supersymmetric models with branes, including applications to brane-world scenarios like Randall-Sundrum models, without fine tuning.

Contribution

It introduces a new construction that incorporates supersymmetry in singular geometries, including the addition of specific fields and the ability to define supersymmetry on orbifolds.

Findings

Supersymmetry can be consistently defined on S_1/Z_2 orbifolds.

Randall-Sundrum brane-worlds are reproducible without fine tuning.

The energy of static configurations vanishes, E=0.

Abstract

We develop the concept of supersymmetry in singular spaces, apply it in an example for 3-branes in D=5 and comment on 8-branes in D=10. The new construction has an interpretation that the brane is a sink for the flux and requires adding to the standard supergravity a (D-1)-form field and a supersymmetry singlet field. This allows a consistent definition of supersymmetry on a S_1/Z_2 orbifold, the bulk and the brane actions being separately supersymmetric. Randall-Sundrum brane-worlds can be reproduced in this framework without fine tuning. For fixed scalars, the doubling of unbroken supersymmetries takes place and the negative tension brane can be pushed to infinity. In more general BPS domain walls with 1/2 of unbroken supersymmetries, the distance between branes in some cases may be restricted by the collapsing cycles of the Calabi-Yau manifold. The energy of any static x^5-dependent bosonic configuration vanishes, E=0, in analogy with the vanishing of the Hamiltonian in a closed universe.