The Final Model Building for the Supersymmetric Pati-Salam Models from Intersecting D6-Branes

TL;DR

This paper demonstrates that string scale gauge coupling unification in supersymmetric Pati-Salam models from intersecting D6-branes can be achieved by adding specific vector-like particles, addressing a key challenge in string phenomenology.

Contribution

It shows how to realize gauge coupling unification at the string scale in intersecting D6-brane models by introducing a precise set of vector-like particles determined by brane intersection numbers.

Findings

Gauge coupling unification achieved at GUT scale via two-loop RGEs.

Seven pairs of vector-like particles introduced from the ${ m N}=2$ sector.

The number of vector-like particles is dictated by brane intersection data.

Abstract

All the possible three-family ${\cal N}=1$ supersymmetric Pati-Salam models constructed with intersecting D6-branes from Type IIA orientifolds on $T^6/(\mathbb{Z}_2\times \mathbb{Z}_2)$ are recently presented in arXiv: 2112.09632. Taking models with largest wrapping number $5$ and approximate gauge coupling unification at GUT scale as examples, we show string scale gauge coupling unification can be realized through two-loop renormalization group equation running by introducing seven pairs of vector-like particles from ${\cal N}=2$ sector. The number of these introduced vector-like particles are fully determined by the brane intersection numbers while there are two D6-brane parallel to each other along one two-torus. We expect this will solve the gauge coupling unification problem in the generic intersecting brane worlds by introducing vector-like particles that naturally included in the ${\cal N}=2$ sector.