Abstract
We construct a systematic method to build all the possible three-family \( \mathcal{N} \) = 1 supersymmetric Pati-Salam models from Type IIA orientifolds on 𝕋6/(ℤ2 × ℤ2) with intersecting D6-branes, in which the SU(4)C × SU(2)L × SU(2)R gauge symmetry can be broken down to the SU(3)C × SU(2)L × U(1)Y Standard Model gauge symmetry by the D-brane splitting and supersymmetry preserving Higgs mechanism. This is essentially achieved by solving all the common solutions for three generation conditions, RR tadpole cancellation conditions, and \( \mathcal{N} \) = 1 supersymmetry conditions with deterministic algorithm. We find that there are 202752 possible supersymmetric Pati-Salam models in total, and show that there are only 33 independent models with different gauge coupling relations at GUTs scale after modding out equivalent relations, such as T-dualities, etc. In particular, there is one and only one independent model which has gauge coupling unification. Furthermore, one can construct other types of intersecting D-brane models utilizing such deterministic algorithm, and therefore we suggest a brand new method for D-brane model building.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C. Angelantonj, M. Bianchi, G. Pradisi, A. Sagnotti and Y.S. Stanev, Chiral asymmetry in four-dimensional open string vacua, Phys. Lett. B 385 (1996) 96 [hep-th/9606169] [INSPIRE].
M. Berkooz and R.G. Leigh, A D = 4 N = 1 orbifold of type-I strings, Nucl. Phys. B 483 (1997) 187 [hep-th/9605049] [INSPIRE].
G. Shiu and S.H.H. Tye, TeV scale superstring and extra dimensions, Phys. Rev. D 58 (1998) 106007 [hep-th/9805157] [INSPIRE].
J.D. Lykken, E. Poppitz and S.P. Trivedi, Branes with GUTs and supersymmetry breaking, Nucl. Phys. B 543 (1999) 105 [hep-th/9806080] [INSPIRE].
M. Cvetič, M. Plümacher and J. Wang, Three family type IIB orientifold string vacua with nonAbelian Wilson lines, JHEP 04 (2000) 004 [hep-th/9911021] [INSPIRE].
M. Cvetič, A.M. Uranga and J. Wang, Discrete Wilson lines in N = 1 D = 4 type IIB orientifolds: A systematic exploration for Z(6) orientifold, Nucl. Phys. B 595 (2001) 63 [hep-th/0010091] [INSPIRE].
G. Aldazabal, A. Font, L.E. Ibáñez and G. Violero, D = 4, N = 1, type IIB orientifolds, Nucl. Phys. B 536 (1998) 29 [hep-th/9804026] [INSPIRE].
G. Aldazabal, L.E. Ibáñez, F. Quevedo and A.M. Uranga, D-branes at singularities: A bottom up approach to the string embedding of the standard model, JHEP 08 (2000) 002 [hep-th/0005067] [INSPIRE].
M. Klein and R. Rabadán, ZN × ZM orientifolds with and without discrete torsion, JHEP 10 (2000) 049 [hep-th/0008173] [INSPIRE].
M. Berkooz, M.R. Douglas and R.G. Leigh, Branes intersecting at angles, Nucl. Phys. B 480 (1996) 265 [hep-th/9606139] [INSPIRE].
C. Bachas, A way to break supersymmetry, hep-th/9503030 [INSPIRE].
J.F.G. Cascales and A.M. Uranga, Chiral 4-D string vacua with D-branes and moduli stabilization, in 10th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories (MG X MMIII), (2003), pp. 1048–1067 [hep-th/0311250] [INSPIRE].
M. Cvetič, T. Li and T. Liu, Supersymmetric Pati-Salam models from intersecting D6-branes: A road to the standard model, Nucl. Phys. B 698 (2004) 163 [hep-th/0403061] [INSPIRE].
C.-M. Chen, T. Li, V.E. Mayes and D.V. Nanopoulos, A realistic world from intersecting D6-branes, Phys. Lett. B 665 (2008) 267 [hep-th/0703280] [INSPIRE].
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 (2008) 125023 [arXiv:0711.0396] [INSPIRE].
C.-M. Chen, T. Li, V.E. Mayes and D.V. Nanopoulos, Variations of the hidden sector in a realistic intersecting brane model, J. Phys. G 35 (2008) 095008 [arXiv:0704.1855] [INSPIRE].
R. Blumenhagen, L. Görlich, B. Körs and D. Lüst, Noncommutative compactifications of type-I strings on tori with magnetic background flux, JHEP 10 (2000) 006 [hep-th/0007024] [INSPIRE].
R. Blumenhagen, B. Körs and D. Lüst, Type I strings with F flux and B flux, JHEP 02 (2001) 030 [hep-th/0012156] [INSPIRE].
G. Aldazabal, S. Franco, L.E. Ibáñez, R. Rabadán and A.M. Uranga, Intersecting brane worlds, JHEP 02 (2001) 047 [hep-ph/0011132] [INSPIRE].
M. Cvetič, G. Shiu and A.M. Uranga, Three family supersymmetric standard-like models from intersecting brane worlds, Phys. Rev. Lett. 87 (2001) 201801 [hep-th/0107143] [INSPIRE].
M. Cvetič, G. Shiu and A.M. Uranga, Chiral four-dimensional N = 1 supersymmetric type 2A orientifolds from intersecting D6 branes, Nucl. Phys. B 615 (2001) 3 [hep-th/0107166] [INSPIRE].
M. Cvetič and I. Papadimitriou, More supersymmetric standard-like models from intersecting D6-branes on type IIA orientifolds, Phys. Rev. D 67 (2003) 126006 [hep-th/0303197] [INSPIRE].
M. Cvetič, I. Papadimitriou and G. Shiu, Supersymmetric three family SU(5) grand unified models from type IIA orientifolds with intersecting D6-branes, Nucl. Phys. B 659 (2003) 193 [Erratum ibid. 696 (2004) 298] [hep-th/0212177] [INSPIRE].
M. Cvetič, P. Langacker and G. Shiu, Phenomenology of a three family standard like string model, Phys. Rev. D 66 (2002) 066004 [hep-ph/0205252] [INSPIRE].
M. Cvetič, P. Langacker and G. Shiu, A three family standard-like orientifold model: Yukawa couplings and hierarchy, Nucl. Phys. B 642 (2002) 139 [hep-th/0206115] [INSPIRE].
M. Cvetič and I. Papadimitriou, Conformal field theory couplings for intersecting D-branes on orientifolds, Phys. Rev. D 68 (2003) 046001 [Erratum ibid. 70 (2004) 029903] [hep-th/0303083] [INSPIRE].
M. Cvetič, P. Langacker and J. Wang, Dynamical supersymmetry breaking in standard-like models with intersecting D6-branes, Phys. Rev. D 68 (2003) 046002 [hep-th/0303208] [INSPIRE].
R. Blumenhagen, L. Görlich and T. Ott, Supersymmetric intersecting branes on the type IIA T6/Z4 orientifold, JHEP 01 (2003) 021 [hep-th/0211059] [INSPIRE].
G. Honecker, Chiral supersymmetric models on an orientifold of Z4 × Z2 with intersecting D6-branes, Nucl. Phys. B 666 (2003) 175 [hep-th/0303015] [INSPIRE].
T.-j. Li and T. Liu, Supersymmetric G3 unification from intersecting D6-branes on type IIA orientifolds, Phys. Lett. B 573 (2003) 193 [hep-th/0304258] [INSPIRE].
M. Cvetič, P. Langacker, T.-j. Li and T. Liu, D6-brane splitting on type IIA orientifolds, Nucl. Phys. B 709 (2005) 241 [hep-th/0407178] [INSPIRE].
C.M. Chen, G.V. Kraniotis, V.E. Mayes, D.V. Nanopoulos and J.W. Walker, A supersymmetric flipped SU(5) intersecting brane world, Phys. Lett. B 611 (2005) 156 [hep-th/0501182] [INSPIRE].
C.M. Chen, G.V. Kraniotis, V.E. Mayes, D.V. Nanopoulos and J.W. Walker, A k-theory anomaly free supersymmetric flipped SU(5) model from intersecting branes, Phys. Lett. B 625 (2005) 96 [hep-th/0507232] [INSPIRE].
C.-M. Chen, T. Li and D.V. Nanopoulos, Standard-like model building on Type II orientifolds, Nucl. Phys. B 732 (2006) 224 [hep-th/0509059] [INSPIRE].
C.-M. Chen, T. Li, V.E. Mayes and D.V. Nanopoulos, Yukawa Corrections from Four-Point Functions in Intersecting D6-Brane Models, Phys. Rev. D 78 (2008) 105015 [arXiv:0807.4216] [INSPIRE].
R. Blumenhagen, M. Cvetič, P. Langacker and G. Shiu, Toward realistic intersecting D-brane models, Ann. Rev. Nucl. Part. Sci. 55 (2005) 71 [hep-th/0502005] [INSPIRE].
R. Blumenhagen, B. Körs, D. Lüst and S. Stieberger, Four-dimensional String Compactifications with D-branes, Orientifolds and Fluxes, Phys. Rept. 445 (2007) 1 [hep-th/0610327] [INSPIRE].
M.R. Douglas and W. Taylor, The landscape of intersecting brane models, JHEP 01 (2007) 031 [hep-th/0606109] [INSPIRE].
T. Li, A. Mansha and R. Sun, Revisiting the supersymmetric Pati-Salam models from intersecting D6-branes, Eur. Phys. J. C 81 (2021) 82 [arXiv:1910.04530] [INSPIRE].
T. Li, A. Mansha, R. Sun, L. Wu and W. He, N = 1 supersymmetric SU(12)C × SU(2)L × SU(2)R models, SU(4)C × SU(6)L × DU(2)R models, and SU(4)C × SU(2)L × SU(6)R models from intersecting D6-branes, Phys. Rev. D 104 (2021) 046018 [INSPIRE].
J. Halverson, B. Nelson and F. Ruehle, Branes with Brains: Exploring String Vacua with Deep Reinforcement Learning, JHEP 06 (2019) 003 [arXiv:1903.11616] [INSPIRE].
G.J. Loges and G. Shiu, Breeding Realistic D-brane Models, Fortsch. Phys. 70 (2022) 2200038 [arXiv:2112.08391] [INSPIRE].
G. Aldazabal, S. Franco, L.E. Ibáñez, R. Rabadán and A.M. Uranga, D = 4 chiral string compactifications from intersecting branes, J. Math. Phys. 42 (2001) 3103 [hep-th/0011073] [INSPIRE].
L.E. Ibáñez, F. Marchesano and R. Rabadán, Getting just the standard model at intersecting branes, JHEP 11 (2001) 002 [hep-th/0105155] [INSPIRE].
T.R. Taylor, Dilaton, gaugino condensation and supersymmetry breaking, Phys. Lett. B 252 (1990) 59 [INSPIRE].
R. Brustein and P.J. Steinhardt, Challenges for superstring cosmology, Phys. Lett. B 302 (1993) 196 [hep-th/9212049] [INSPIRE].
B. de Carlos, J.A. Casas and C. Muñoz, Supersymmetry breaking and determination of the unification gauge coupling constant in string theories, Nucl. Phys. B 399 (1993) 623 [hep-th/9204012] [INSPIRE].
W. He, T. Li, R. Sun and L. Wu, The Final Model Building for the Supersymmetric Pati-Salam Models from Intersecting D6-branes, arXiv:2112.09630 [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2112.09632
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
He, W., Li, T. & Sun, R. The complete search for the supersymmetric Pati-Salam models from intersecting D6-branes. J. High Energ. Phys. 2022, 44 (2022). https://doi.org/10.1007/JHEP08(2022)044
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2022)044