A WAY TO BREAK SUPERSYMMETRY

TL;DR

This paper explores a novel mechanism for spontaneous supersymmetry breaking via magnetized compactifications in string theory, which can produce the Standard Model gauge group, chiral families, and electroweak symmetry breaking, while discussing related theoretical challenges.

Contribution

It introduces a new compactification approach that breaks supersymmetry spontaneously through magnetic fields, linking gauge symmetry breaking with the generation of chiral fermions and the Standard Model.

Findings

Magnetic compactifications can reconcile chirality with extended supersymmetry.

They can trigger gauge symmetry breaking at a scale related to supersymmetry breaking.

The model produces three chiral families and the Standard Model gauge group.

Abstract

I study the spontaneous breakdown of supersymmetry when higher-dimensional Yang-Mills or the type-I $SO(32)$ string theory are compactified on magnetized tori. Because of the universal gyromagnetic ratio $g=2$, the splittings of all multiplets are given by the product of charge times internal helicity operators. As a result such compactifications have two remarkable and robust features: {\it (a)} they can reconcile {\it chirality} with {\it extended} low-energy supersymmetry in the limit of large tori, and {\it (b)} they can trigger gauge-symmetry breaking, via Nielsen-Olesen instabilities, at a scale tied classically to $m_{SUSY}$. I exhibit a compactification of the $SO(32)$ superstring, in which magnetic fields break spontaneously $N=4$ supersymmetry, produce the standard-model gauge group with three chiral families of quarks and leptons, and trigger electroweak symmetry breaking. I discuss supertrace relations and the ensuing ultraviolet softness. As with other known mechanisms of supersymmetry breaking, the one proposed here faces two open problems: the threat to perturbative calculability in the decompactification limit, and the problem of gravitational stability and in particular of the cosmological constant. I explain, however, why a good classical description of the vacuum may require small tadpoles for the dilaton, moduli and metric.