String-scale Gauge Coupling Relations in the Supersymmetric Pati-Salam Models from Intersecting D6-branes

TL;DR

This paper constructs supersymmetric Pati-Salam models from intersecting D6-branes and demonstrates how to achieve gauge coupling unification at the string scale through two-loop RGE running, addressing a key challenge in string phenomenology.

Contribution

It provides a method to realize string-scale gauge coupling relations in intersecting D-brane models by analyzing particle decoupling and RGE running.

Findings

33 independent models constructed

Gauge coupling relations achieved via two-loop RGE

Decoupling of exotic particles successfully implemented

Abstract

We have constructed all the three-family ${\cal N} = 1$ supersymmetric Pati-Salam models from intersecting D6-branes, and obtained 33 independent models in total. But how to realize the string-scale gauge coupling relations in these models is a big challenge. We first discuss how to decouple the exotic particles in these models. In addition, we consider the adjoint chiral mulitplets for $SU(4)_C$ and $SU(2)_L$ gauge symmetries, the Standard Model (SM) vector-like particles from D6-brane intersections, as well as the vector-like particles from the ${\cal N}=2$ subsector. We show that the gauge coupling relations at string scale can be achieved via two-loop renormalization group equation running for all these supersymmetric Pati-Salam models. Therefore, we propose a concrete way to obtain the string-scale gauge coupling realtions for the generic intersecting D-brane models.