Intersecting branes, Higgs sector, and chirality from $\mathcal{N}=4$ SYM with soft SUSY breaking

TL;DR

This paper explores how soft SUSY breaking in $ ext{SU}(N)$ $ ext{N}=4$ SYM leads to intersecting brane configurations with chiral fermions and Higgs-induced Yukawa couplings, resembling features of the Standard Model.

Contribution

It uncovers exact brane solutions with Higgs condensates that generate Yukawa couplings and chiral gauge theories, closely resembling Standard Model-like physics.

Findings

Exact solutions with intersecting branes and Higgs condensates.

Yukawa couplings between chiral fermionic zero modes.

Gauge fields coupling to chiral fermions similar to Standard Model.

Abstract

We consider $SU(N)$ $\mathcal{N}=4$ super Yang-Mills with cubic and quadratic soft SUSY breaking potential, such that the global $SU(4)_R$ is broken to $SU(3)$ or further. As shown recently, this set-up supports a rich set of non-trivial vacua with the geometry of self-intersecting $SU(3)$ branes in 6 extra dimensions. The zero modes on these branes can be interpreted as 3 generations of bosonic and chiral fermionic strings connecting the branes at their intersections. Here, we uncover a large class of exact solutions consisting of branes connected by Higgs condensates, leading to Yukawa couplings between the chiral fermionic zero modes. Under certain decoupling conditions, the backreaction of the Higgs on the branes vanishes exactly. The resulting physics is that of a spontaneously broken chiral gauge theory on branes with fluxes. In particular, we identify combined brane plus Higgs configurations which lead to gauge fields that couple to chiral fermions at low energy. This turns out to be quite close to the Standard Model and its constructions via branes in string theory. As a by-product, we construct a $G_2$-brane solution corresponding to a squashed fuzzy coadjoint orbit of $G_2$.