SUSY Quivers, Intersecting Branes and the Modest Hierarchy Problem

TL;DR

The paper proposes a class of four-dimensional, chiral, non-supersymmetric field theories with quadratic divergences suppressed up to two loops, realized as SUSY quivers where ${\cal N}=4$ gauge nodes connect via bifundamental chiral multiplets that preserve different ${\cal N}=1$ subgroups. These Q-SUSY theories are naturally embedded in Type II string theory as D6-branes at angles on a six-torus, with gauge couplings and FI-terms derivable from the Born-Infeld action and RR/NSNS couplings, and with consistency conditions provided by RR/NS tadpole cancellation. The authors construct explicit D6-brane models, including MSSM-like spectra with three generations, where a modest hierarchy between a string scale around $M_s\sim 10$–$100$ TeV and the weak scale is stabilized by two-loop protection and geometric recombination of branes for electroweak symmetry breaking. While NS-NS tadpoles introduce instabilities in general, the Q-SUSY framework yields a simplified scalar potential and controlled SUSY breaking, offering a concrete phenomenological avenue for low-scale string scenarios with reduced fine-tuning and interesting collider implications.

Abstract

We present a class of chiral non-supersymmetric D=4 field theories in which quadratic divergences appear only at two loops. They may be depicted as ``SUSY quivers'' in which the nodes represent a gauge group with extended e.g., N=4 SUSY whereas links represent bifundamental matter fields which transform as chiral multiplets with respect to different N=1 subgroups. One can obtain this type of field theories from simple D6-brane configurations on Type IIA string theory compactified on a six-torus. We discuss the conditions under which this kind of structure is obtained from D6-brane intersections. We also discuss some aspects of the effective low-energy field theory. In particular we compute gauge couplings and Fayet-Iliopoulos terms from the Born-Infeld action and show how they match the field theory results. This class of theories may be of phenomenological interest in order to understand the modest hierarchy problem i.e., the stability of the hierarchy between the weak scale and a fundamental scale of order 10-100 TeV which appears e.g. in low string scale models. Specific D-brane models with the spectrum of the SUSY Standard Model and three generations are presented.