Intersecting Brane Models of Particle Physics and the Higgs Mechanism

TL;DR

This work embeds the Standard Model within Type IIA intersecting D6-brane constructions on a toroidal orientifold, using four-stack quivers to realize three generations with quasi-supersymmetry. It recasts electroweak symmetry breaking as a geometric brane recombination process, where U(2)_L × U(1) collate into a single brane corresponding to U(1)_em, and analyzes how SUSY at intersections (or its absence) shapes the Higgs sector, FI-terms, and neutrino masses. The authors construct explicit square, linear, rombic, and triangle quivers, study their U(1) massless spectra, and derive gauge-coupling relations via wrapped cycle volumes, highlighting how B-L generically survives as a massless gauge symmetry in many Q-SUSY setups and how B-L breaking via brane recombination can yield Majorana neutrino masses. Together, these results offer a concrete string-based mechanism for the SM Higgs sector, hierarchies at low string scales, and neutrino mass generation, with testable implications for the structure of Abelian gauge groups and scalar masses in D-brane worlds.

Abstract

We analyze a recently constructed class of D-brane theories with the fermion spectrum of the SM at the intersection of D6-branes wrapping a compact toroidal space. We show how the SM Higgs mechanism appears as a brane recombination effect in which the branes giving rise to U(2)_L \times U(1) recombine into a single brane related to U(1)_{em}. We also show how one can construct D6-brane models which respect some supersymmetry at every intersection. These are quasi-supersymmetric models of the type introduced in hep-th/0201205 which may be depicted in terms of SUSY-quivers and may stabilize the hierarchy between the weak scale and a fundamental scale of order 10-100 TeV present in low string scale models. Several explicit D6-brane models with three generations of quarks and leptons and different SUSY-quiver structure are presented. One can prove on general grounds that if one wants to build a (factorizable) D6-brane configuration with the SM gauge group and N = 1 SUSY (or quasi-SUSY), also a massless (B-L) generator must be initially present in any model. If in addition we insist on lef- and right-handed fermions respecting the same N=1 SUSY, the brane configurations are forced to have intersections giving rise to Higgs multiplets, providing for a rationale for the very existence of the SM Higgs sector.