Open Access

Three-family supersymmetric Pati-Salam flux models from rigid D-branes

Adeel Mansha^1,*, Mudassar Sabir ^2,†, Tianjun Li^3,‡, and Luyang Wang^1,§

¹College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, People’s Republic of China
²School of Physics, University of Electronic Science and Technology of China, 2006 Xiyuan Avenue, Chengdu, People’s Republic of China
³School of Physics, Henan Normal University, Xinxiang 453007, People’s Republic of China

^*Contact author: adeelmansha@alumni.itp.ac.cn
^†Contact author: mudassar.sabir@uestc.edu.cn
^‡Contact author: tli@itp.ac.cn
^§Contact author: wangly@szu.edu.cn

Phys. Rev. D 113, 115033 – Published 15 June, 2026

DOI: https://doi.org/10.1103/zq28-j515

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 [Phys. Rev. D 112, 055006 (2025)], this issue was resolved by employing the rigid D6-branes on the $T^{6} / (Z_{2} \times Z_{2}^{'})$ 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 $T^{6} / (Z_{2} \times Z_{2})$ , 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 $N = 1$ 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.

Physics Subject Headings (PhySH)

Article Text

References (45)

M. Cvetic, T. Li, and T. Liu, Supersymmetric Pati-Salam models from intersecting D6-branes: A road to the standard model, Nucl. Phys. B698, 163 (2004).
C.-M. Chen, T. Li, V. E. Mayes, and D. V. Nanopoulos, Towards realistic supersymmetric spectra and Yukawa textures from intersecting branes, Phys. Rev. D 77, 125023 (2008).
T. Li, A. Mansha, and R. Sun, Revisiting the supersymmetric Pati–Salam models from intersecting D6-branes, Eur. Phys. J. C 81, 82 (2021).
T. Li, A. Mansha, R. Sun, L. Wu, and W. He, $N = 1$ supersymmetric $S U (12)_{C} \times S U (2)_{L} \times S U (2)_{R}$ models, $S U (4)_{C} \times S U (6)_{L} \times S U (2)_{R}$ models, and $S U (4)_{C} \times S U (2)_{L} \times S U (6)_{R}$ models from intersecting D6-branes, Phys. Rev. D 104, 046018 (2021).
M. Sabir, T. Li, A. Mansha, and X.-C. Wang, The supersymmetry breaking soft terms, and fermion masses and mixings in the supersymmetric Pati-Salam model from intersecting D6-branes, J. High Energy Phys. 04 (2022) 089.
A. Mansha, T. Li, M. Sabir, and L. Wu, Three-family supersymmetric Pati–Salam models with symplectic groups from intersecting D6-branes, Eur. Phys. J. C 84, 151 (2024).
A. Mansha, T. Li, and L. Wu, The hidden sector variations in the $N = 1$ supersymmetric three-family Pati–Salam models from intersecting D6-branes, Eur. Phys. J. C 83, 1067 (2023).
A. Mansha, T. Li, and M. Sabir, Revisiting the supersymmetric trinification models from intersecting D6-branes, Commun. Theor. Phys. 76, 095201 (2024).
W. He, T. Li, R. Sun, and L. Wu, The final model building for the supersymmetric Pati–Salam models from intersecting D6-branes, Eur. Phys. J. C 82, 710 (2022).
M. Sabir, A. Mansha, T. Li, and Z.-W. Wang, Fermion masses and mixings in the supersymmetric Pati-Salam landscape from Intersecting D6-Branes, J. High Energy Phys. 10 (2024) 252.
M. Sabir, A. Mansha, T. Li, and Z.-W. Wang, Susy breaking soft terms in the supersymmetric Pati-Salam landscape from intersecting D6-branes, J. High Energy Phys. 01 (2024) 201.
M. Sabir, A. Mansha, T. Li, and Z.-W. Wang, Fermion masses and mixings in string theory with Dirac neutrinos, Phys. Rev. D 111, L071702 (2025).
R. Blumenhagen, M. Cvetic, F. Marchesano, and G. Shiu, Chiral D-brane models with frozen open string moduli, J. High Energy Phys. 03 (2005) 050.
A. Mansha, M. Sabir, T. Li, and L. Wang, Three-family supersymmetric Pati-Salam models from intersecting D6-branes on rigid cycles, Phys. Rev. D 112, 055006 (2025).
A. Mansha, M. Sabir, T. Li, and L. Wang, Three family supersymmetric Pati-Salam model from rigid intersecting D6-branes, Phys. Rev. D 111, L121904 (2025).
R. Blumenhagen, D. Lust, and T. R. Taylor, Moduli stabilization in chiral type IIB orientifold models with fluxes, Nucl. Phys. B663, 319 (2003).
J. F. G. Cascales and A. M. Uranga, Chiral 4d string vacua with D branes and NSNS and RR fluxes, J. High Energy Phys. 05 (2003) 011.
F. Marchesano and G. Shiu, Building MSSM flux vacua, J. High Energy Phys. 11 (2004) 041.
M. Cvetic, T. Li, and T. Liu, Standard-like models as type IIB flux vacua, Phys. Rev. D 71, 106008 (2005).
C.-M. Chen, T. Li, and D. V. Nanopoulos, Standard-like model building on type II orientifolds, Nucl. Phys. B732, 224 (2006).
C.-M. Chen, T. Li, and D. V. Nanopoulos, Type IIA Pati-Salam flux vacua, Nucl. Phys. B740, 79 (2006).
C.-M. Chen, T. Li, Y. Liu, and D. V. Nanopoulos, Realistic type IIB supersymmetric Minkowski flux vacua, Phys. Lett. B 668, 63 (2008).
C.-M. Chen, S. Hu, T. Li, and D. V. Nanopoulos, Type IIB supersymmetric flux vacua, arXiv:1107.3465.
R. Blumenhagen, B. Kors, D. Lust, and S. Stieberger, Four-dimensional string compactifications with D-branes, orientifolds and fluxes, Phys. Rep. 445, 1 (2007).
R. Blumenhagen, B. Kors, D. Lust, and T. Ott, The standard model from stable intersecting brane world orbifolds, Nucl. Phys. B616, 3 (2001).
R. Blumenhagen, L. Gorlich, and T. Ott, Supersymmetric intersecting branes on the type IIA $T^{6} / Z_{2}$ orientifold, J. High Energy Phys. 01 (2003) 021.
R. Blumenhagen, M. Cvetic, P. Langacker, and G. Shiu, Toward realistic intersecting D-brane models, Annu. Rev. Nucl. Part. Sci. 55, 71 (2005).
M. Cvetic, G. Shiu, and A. M. Uranga, Chiral four-dimensional $N = 1$ supersymmetric type 2A orientifolds from intersecting D6 branes, Nucl. Phys. B615, 3 (2001).
C. Angelantonj, I. Antoniadis, G. D’Appollonio, E. Dudas, and A. Sagnotti, Type I vacua with brane supersymmetry breaking, Nucl. Phys. B572, 36 (2000).
M. Grana, Flux compactifications in string theory: A comprehensive review, Phys. Rep. 423, 91 (2006).
S. Kachru, R. Kallosh, A. D. Linde, and S. P. Trivedi, De Sitter vacua in string theory, Phys. Rev. D 68, 046005 (2003).
S. Forste and G. Honecker, Rigid D6-branes on $T^{6} / (Z_{2} \times Z_{2 M} \times Ω R)$ with discrete torsion, J. High Energy Phys. 01 (2010) 091.
M. Cvetic, P. Langacker, and J. Wang, Dynamical supersymmetry breaking in standard—like models with intersecting D6-branes, Phys. Rev. D 68, 046002 (2003).
D. Lust, P. Mayr, R. Richter, and S. Stieberger, Scattering of gauge, matter, and moduli fields from intersecting branes, Nucl. Phys. B696, 205 (2004).
P. H. Ginsparg, Gauge and Gravitational Couplings in Four-Dimensional String Theories, Phys. Lett. B 197, 139 (1987).
Y. Hamada, T. Kobayashi, and S. Uemura, Standard Model-like D-brane models and gauge couplings, Nucl. Phys. B897, 563 (2015).
K. R. Dienes and J. March-Russell, Realizing higher level gauge symmetries in string theory: New embeddings for string GUTs, Nucl. Phys. B479, 113 (1996).
M. B. Green and J. H. Schwarz, Anomaly cancellation in supersymmetric $D = 10$ gauge theory and superstring theory, Phys. Lett. 149B, 117 (1984).
F. Marchesano and G. Shiu, MSSM vacua from flux compactifications, Phys. Rev. D 71, 011701 (2005).
A. M. Uranga, D-brane probes, RR tadpole cancellation and K-theory charge, Nucl. Phys. B598, 225 (2001).
S. Gukov, C. Vafa, and E. Witten, CFT’s from Calabi-Yau four folds, Nucl. Phys. B584, 69 (2000); B608, 477(E) (2001).
M. R. Douglas and S. Kachru, Flux compactification, Rev. Mod. Phys. 79, 733 (2007).
S. B. Giddings, S. Kachru, and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66, 106006 (2002).
S. Forste and I. Zavala, Oddness from Rigidness, J. High Energy Phys. 07 (2008) 086.
W. He, T. Li, and R. Sun, The complete search for the supersymmetric Pati-Salam models from intersecting D6-branes, J. High Energy Phys. 08 (2021) 044.

Phys. Rev. D 113, 115033– Published 15 June, 2026

Vol. 113, Iss. 11 — 1 June 2026

Received 29 January 2026
Accepted 11 May 2026

DOI: https://doi.org/10.1103/zq28-j515

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physical Review D

Reuse & Permissions

Export citation

Export citation

Three-family supersymmetric Pati-Salam flux models from rigid D-branes

Abstract

Physics Subject Headings (PhySH)

Article Text

References (45)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation