GUT Model Hierarchies from Intersecting Branes

TL;DR

This work constructs the first three-generation string GUTs based on the Pati–Salam gauge group $SU(4)_C \times SU(2)_L \times SU(2)_R$ from D6-branes intersecting at angles in Type I orientifolds, yielding the Standard Model spectrum at low energy. A generalized Green–Schwarz mechanism cancels U(1) anomalies, leaving a gauged baryon number and an anomaly-free U(1) that can survive to low energies, with models categorized as PS-A (SM at low energy) or PS-B (SM plus extra U(1)); multiwrapping effects are shown to be field redefinitions of the surviving U(1). In the PS-A class, imposing SUSY at specific intersections generates scalar partners and Majorana masses for right-handed neutrinos, enabling a see-saw mechanism and predicting light left-handed doublets that constrain the string scale to $M_s \lesssim 650$ GeV, making the framework directly testable at colliders; the neutrino mass hierarchy can accommodate $m_\nu$ in the $0.1$–$10$ eV range consistent with oscillation data, while preserving proton stability via gauged baryon number. The model also reproduces the GUT relation $m_e = m_d$ at the GUT scale and provides a general gauge-breaking mechanism applicable to left–right symmetric models. Overall, these PS-based intersecting-brane constructions offer a concrete, testable route to string-derived GUTs with realistic low-energy phenomenology and characteristic collider signatures.

Abstract

By employing D6-branes intersecting at angles in $D = 4$ type I strings, we construct the first examples of three generation string GUT models (PS-A class), that contain at low energy exactly the standard model spectrum with no extra matter and/or extra gauge group factors. They are based on the group $SU(4)_C \times SU(2)_L \times SU(2)_R$. The models are non-supersymmetric, even though SUSY is unbroken in the bulk. Baryon number is gauged and its anomalies are cancelled through a generalized Green-Schwarz mechanism. We also discuss models (PS-B class) which at low energy have the standard model augmented by an anomaly free U(1) symmetry and show that multibrane wrappings correspond to a trivial redefinition of the surviving global U(1) at low energies. There are no colour triplet couplings to mediate proton decay and proton is stable. The models are compatible with a low string scale of energy less that 650 GeV and are directly testable at present or future accelerators as they predict the existence of light left handed weak fermion doublets at energies between 90 and 246 GeV. The neutrinos get a mass through an unconventional see-saw mechanism. The mass relation $m_e = m_d$ at the GUT scale is recovered. Imposing supersymmetry at particular intersections generates non-zero Majorana masses for right handed neutrinos as well providing the necessary singlets needed to break the surviving anomaly free U(1), thus suggesting a gauge symmetry breaking method that can be applied in general left-right symmetric models.

Figures (2)

• Figure 1: Assignment of angles between D6-branes on a a type I PS-A class of models based on the initial gauge group $U(4)_C\times {U(2)}_L\times {U(2)}_R$. The angles between branes are shown on a product of $T^2 \times T^2 \times T^2$. We have chosen $\beta_1 =1$, $m_b^1, m_c^1, n_a^2 >0$, $\epsilon = {\tilde{\epsilon}}= 1$. These models break to low energies to exactly the SM.
• Figure 2: Assignment of angles between D6-branes on a a type I PS-B class of models based on the initial gauge group $U(4)_C\times {U(2)}_L\times {U(2)}_R$. The angles between branes are shown on a product of $T^2 \times T^2 \times T^2$. We have chosen $\rho = \beta_1 =1$, $n_b^1, n_c^1, n_a^2, n_d^2 >0$, $\epsilon = 1$. These models break to low energy to the SM augmented by an anomaly free $U(1)$ symmetry.