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Three-Family Supersymmetric Pati-Salam Flux Models from Rigid D-Branes

Adeel Mansha, Mudassar Sabir, Tianjun Li, Luyang Wang

TL;DR

This work develops three-family, $\mathcal{N}=1$ Pati–Salam flux vacua by embedding rigid D-branes in Type IIB on $\mathbb{T}^6/(\mathbb{Z}_2\times\mathbb{Z}_2)$, leveraging a quantized $G_3$ flux to stabilize complex structure and the axio-dilaton. The construction is T-dual to Type IIA models with discrete torsion and utilizes exotic O3$^{++}$-planes to realize rigid cycles, thereby eliminating open-string adjoint moduli. The models satisfy $\mathcal{N}=1$ SUSY, RR tadpole cancellation with flux, and K-theory constraints, and yield complete spectra with three chiral families that can break to the Standard Model via a SUSY-preserving Higgs mechanism; exotic states decouple through strong hidden-sector dynamics. A thorough beta-function analysis reveals that asymptotic freedom is achieved only in a subset of models, guiding phenomenological viability. The results demonstrate a robust framework for simultaneous open- and closed-string moduli stabilization in chiral flux vacua with potential for further Yukawa and SUSY-breaking studies.

Abstract

Intersecting D-brane model building often suffer from the unstabilized open-string moduli, leading to the unwanted massless adjoint scalars. In our previous work arXiv:2505.03664, this issue was resolved by employing the rigid D6-branes on the $\mathbb{T}^6/(\mathbb{Z}_2 \times \mathbb{Z}_2^\prime)$ orientifold with discrete torsion, where fractional cycles eliminate all adjoint scalars. In this paper, we construct new three-family flux models in the Type IIB setup on $\mathbb{T}^6/(\mathbb{Z}_2 \times \mathbb{Z}_2)$, T-dual to the Type IIA rigid D6-brane construction with discrete torsion, by introducing the quantized background $G_3$ flux that stabilizes the closed-string complex structure moduli and axio-dilaton. The resulting Pati-Salam gauge symmetry can be spontaneously broken down to the Standard Model via a supersymmetry-preserving Higgs mechanism. All the consistency conditions, including $\mathcal{N}=1$ supersymmetry, RR tadpole cancellation, and K-theory constraints, are satisfied. We present the complete particle spectra for these models and discuss how exotic states dynamically decouple through strong dynamics in the hidden sector.

Three-Family Supersymmetric Pati-Salam Flux Models from Rigid D-Branes

TL;DR

This work develops three-family, Pati–Salam flux vacua by embedding rigid D-branes in Type IIB on , leveraging a quantized flux to stabilize complex structure and the axio-dilaton. The construction is T-dual to Type IIA models with discrete torsion and utilizes exotic O3-planes to realize rigid cycles, thereby eliminating open-string adjoint moduli. The models satisfy SUSY, RR tadpole cancellation with flux, and K-theory constraints, and yield complete spectra with three chiral families that can break to the Standard Model via a SUSY-preserving Higgs mechanism; exotic states decouple through strong hidden-sector dynamics. A thorough beta-function analysis reveals that asymptotic freedom is achieved only in a subset of models, guiding phenomenological viability. The results demonstrate a robust framework for simultaneous open- and closed-string moduli stabilization in chiral flux vacua with potential for further Yukawa and SUSY-breaking studies.

Abstract

Intersecting D-brane model building often suffer from the unstabilized open-string moduli, leading to the unwanted massless adjoint scalars. In our previous work arXiv:2505.03664, this issue was resolved by employing the rigid D6-branes on the orientifold with discrete torsion, where fractional cycles eliminate all adjoint scalars. In this paper, we construct new three-family flux models in the Type IIB setup on , T-dual to the Type IIA rigid D6-brane construction with discrete torsion, by introducing the quantized background flux that stabilizes the closed-string complex structure moduli and axio-dilaton. The resulting Pati-Salam gauge symmetry can be spontaneously broken down to the Standard Model via a supersymmetry-preserving Higgs mechanism. All the consistency conditions, including supersymmetry, RR tadpole cancellation, and K-theory constraints, are satisfied. We present the complete particle spectra for these models and discuss how exotic states dynamically decouple through strong dynamics in the hidden sector.
Paper Structure (40 sections, 81 equations, 1 figure, 55 tables)

This paper contains 40 sections, 81 equations, 1 figure, 55 tables.

Table of Contents

  1. Introduction
  2. Flux model building on rigid cycles
  3. Untwisted sector and 4D $\mathcal{N}=2$ multiplets
  4. Twisted sectors and fractional branes
  5. Spectrum from rigid branes (η = -1)
  6. Orientifold action
  7. Gauge couplings from complex structure moduli
  8. Supersymmetry conditions
  9. Tadpole cancellation
  10. T-dual Type IIB flux-induced stabilization
  11. Three-form fluxes and the Gukov--Vafa--Witten superpotential
  12. Flux contribution to the D3-brane tadpole
  13. Explicit ISD $(2,1)$ flux and primitivity
  14. Couplings of $G_3$ to $C_4$ in Type IIB supergravity
  15. Magnetized D-branes and T-duality
  16. ...and 25 more sections

Figures (1)

  • Figure 1: The $\mathbb{Z}_2$ invariant a-type (left) and b-type (right) lattices. $\mathbb{Z}_2$ fixed points $\{1,2,3,4\}$ are shown as blobs. The $\mathcal{R}$ invariant $x^i$ axis is along the 1-cycle $[a^i] - \frac{\beta^i}{2} [b^i]$ with $\beta^i=0$ for the a-type lattice and $\beta^i=1$ for the b-type lattice. $\mathcal{R}$ acts as reflection along the $y^i$ axis, which is spanned by the 1-cycle $[b^i]$. For the a-type lattice, all $\mathbb{Z}_2$ fixed points are invariant under $\mathcal{R}$, whereas for the b-type lattice, only 1 and 2 are invariant while $3 \stackrel\mathcal{R}{\leftrightarrow} 4$.