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REVIEW 2 major objections 3 minor 54 references

Three-family supersymmetric Pati-Salam models from intersecting D6-branes on rigid cycles

T0 review · 2 major / 3 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Rigid intersecting D6-branes on a factorizable orientifold with discrete torsion produce the first ten consistent three-family supersymmetric Pati-Salam vacua.

desk verdict Real step toward three-family rigid-brane Pati-Salam models, but the missing fixed-point data makes the consistency claim unverifiable as written. read the letter →

arxiv 2505.03664 v3 pith:FJQFAPCE submitted 2025-05-06 hep-th hep-ph

Adeel Mansha , Mudassar Sabir , Tianjun Li , Luyang Wang This is my paper · ORCID
classification hep-thhep-ph
keywords intersectingD6-branesrigidcyclesPati-Salammodelsdiscretetorsionorientifoldcompactificationthree-familyasymptoticfreedomswamplandbounds
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper claims that rigid intersecting D6-branes on the factorizable $\mathbb{T}^6/(\mathbb{Z}_2\times\mathbb{Z}_2')$ orientifold with discrete torsion can yield ten three-family $\mathcal{N}=1$ supersymmetric Pati-Salam models. Rigid cycles freeze the open-string moduli that would otherwise produce adjoint fields, and the paper's new ingredient is a combination of rigid visible branes with semi-rigid and non-rigid hidden branes plus hidden-brane displacement to cancel tadpoles and remove unwanted matter. Four of the ten models have a negative one-loop $\beta$ coefficient for $SU(4)_C$, hence an asymptotically free color factor. If the construction is right, these are explicit, checkable string vacua with exactly three chiral families and no adjoint exotics.

What carries the argument

The load-bearing object is the rigid fractional D6-brane cycle $$\Pi_a=\frac14\Pi_a^B+\frac14\sum_{(i,j)\in S_a^\$\theta$}\epsilon^\theta_{a,ij}\Pi^\theta_{ij,a}+\cdots$$ a bulk factorizable 3-cycle combined with collapsed cycles at the fixed points the brane passes through, with orientation signs $\epsilon=\pm1$. Rigidity means the brane is stuck at fixed points, so no adjoint chiral multiplets appear. The degree of overlap of fixed-point sets, $\delta^g_{ab}$, controls the chiral intersection numbers; the hidden stacks are displaced to alternative fixed points to force the unwanted $\delta$'s to vanish; and the tadpole and K-theory equations select the allowed multiplicities.

What would settle it

Recompute the twisted tadpole sums (2.30) for one model, say r06, using explicit fixed-point sets $S^g_a$ that match the wrapping numbers in table 23; any nonzero total twisted charge at a fixed point would disprove the model. A second decisive check is to compute the one-loop $\beta$ functions of the hidden confining groups: a positive coefficient would undermine the claimed confinement and decoupling of the exotic states.

Watch

Extended reading notes

Core claim

The discovery is that the obstruction to three families on factorizable tori with rigid branes can be bypassed by adding a fourth visible stack $d$, so the family condition becomes $I_{ab}+I_{ab'}=-(I_{ac}+I_{ac'}+I_{ad}+I_{ad'})=\pm3$, and by allowing the hidden stacks to sit at alternative fixed points rather than the origin. The paper presents ten explicit wrapping-number choices, tables their chiral spectra, and checks $\mathcal{N}=1$ supersymmetry, RR tadpole cancellation, K-theory constraints, and the swampland rank bound. The spectra contain the Pati-Salam matter $(4,2,1,1)$ and $(\bar4,1,2,1)$ plus GUT Higgs pairs obtained by recombining a hidden stack with the $SU(2)_R$ stack, so the Pati-Salam symmetry can break to the Standard Model.

Load-bearing premise

The tabulated spectra and the three-family count rely on the unstated displacement of hidden-sector branes to alternative orbifold fixed points; the paper asserts this removes unwanted massless states and preserves twisted tadpole cancellation, but the concrete fixed-point assignments are not listed, and the twisted tadpole conditions (2.30) depend on exactly those assignments.

Editorial extensions

If this is right

  • These ten models are explicit examples in which Pati-Salam symmetry can break to the Standard Model through the provided $\Delta$ and $\Phi$ Higgs fields while preserving $\mathcal{N}=1$ supersymmetry.
  • In models r19, r20, r25, and r26 the $SU(4)_C$ one-loop beta coefficient is $-2$, $-2$, $-4$, and $-2$ respectively, so the color factor is asymptotically free; the other models have coefficient $+2$.
  • The absence of adjoint chiral multiplets removes the usual obstruction to negative beta functions, making gaugino condensation in the hidden sector a plausible supersymmetry-breaking mechanism.
  • All models satisfy the swampland bound on maximal gauge-group rank, so they are not excluded by that consistency criterion.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The displacement step is not fully specified: the paper's spectra depend on moving hidden branes to alternative fixed points, but the concrete fixed-point sets are not tabulated; a complete check would require listing them and recomputing the twisted tadpole sums (2.30).
  • If the displacement can be realized, the same construction may extend to tilted tori, but the paper notes that no tilted-torus three-family model is known in this framework, so the apparent obstruction remains unexplained.
  • A natural next test is to run the open-string one-loop partition function for the hidden stacks to verify the claimed confinement of every exotic $X$ state; the paper asserts confinement but does not compute the hidden-sector beta functions.
  • The framework suggests a systematic computer search over wrapping numbers and fixed-point assignments; the class is small enough for an exhaustive enumeration rather than only a sampling.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 3 minor

Summary. The paper claims to construct, for the first time, a class of ten three-family N=1 supersymmetric Pati-Salam models from rigid intersecting D6-branes on the factorizable T^6/(Z2 x Z2') orientifold with discrete torsion, using rectangular tori only. Section 2 reviews the standard machinery for such models: fractional brane cycles (2.10), intersection numbers, supersymmetry conditions (2.28), tadpole conditions (2.30), and K-theory constraints (2.32). Section 3 presents ten models (r06, r08, r10, r19, r20, r22, r25, r26, r29, r30) with wrapping numbers in Appendix A and chiral spectra in Tables 4-22, including GUT Higgs fields and exotic states. Section 4 computes one-loop beta-function coefficients for the visible SU(4)_C factor, finding negative values in four models. The paper also claims that hidden-sector strong dynamics confines and decouples exotic states.

Significance. If the consistency of these models could be verified from the data provided, this would be a notable step in string model building: explicit vacua with frozen open-string moduli (no adjoint exotics), three chiral families, and, in models r19, r20, r25 and r26, an asymptotically free SU(4)_C. The paper is transparent in providing complete wrapping numbers for all ten models, and the beta-function values in (4.8) are internally consistent with the intersection numbers in the spectrum tables. The three-family condition is imposed during construction rather than predicted, which is standard model-building practice, and the asymptotic-freedom check is reported for all models, including the six that fail, so there is no selection bias. The main shortcoming is that the models are incompletely specified: the fixed-point and epsilon data needed to verify twisted tadpole cancellation and the chiral spectra are not given, and the hidden-sector confinement is asserted without any dynamical calculation.

major comments (2)
  1. [§3 (Note paragraph) and §2, Eqs. (2.10), (2.30)] Section 3 states that hidden-sector branes are 'displaced ... to alternative orbifold fixed points' to remove unwanted massless matter, but neither the fixed-point sets S^g_a nor the signs ε^g_a,ij required in Eq. (2.10) are specified for any stack. These data enter the twisted-tadpole conditions (2.30) and the intersection numbers (2.11)-(2.19), hence the chiral spectra in Tables 4-22 and the three-family count (2.24). Without these data the reader cannot verify the claimed cancellation of twisted tadpoles or reproduce the tabulated spectra; the central existence claim in the abstract is therefore not independently checkable from the manuscript as written.
  2. [§3 (end of model-building strategy) and Tables 6-22, §4] The decoupling of exotic states is presented as a consequence of hidden-sector strong dynamics, with 'confined spectra' tabulated. However, no beta-function or confinement scale is computed for any hidden gauge factor. The only explicit beta-function calculation in §4, Eq. (4.8), applies to the visible SU(4)_C, and the claim that 'the SU(4) gauge groups in the hidden sector exhibit negative beta functions' is not demonstrated. The confinement assertion is therefore unsupported and should either be backed by explicit hidden-sector beta-function computations or reformulated as a conditional assumption.
minor comments (3)
  1. [Eq. (4.7)] The displayed formula for N_chiral^a lists |I_ad'| twice and omits |I_ad|; the numerical results in (4.8) are consistent with the corrected expression, so this is a typo, but it should be fixed.
  2. [§3.1 and §3.2] The phrase 'share the same fixed points, i.e., δ^g_ab ≠ (4,4,4)' is self-contradictory; presumably it should read 'do not share all their fixed points'.
  3. [Table 2] Table 2 appears malformed in the manuscript: the representation labels (symmetric and antisymmetric) are missing and the multiplicity column contains only intersection expressions, making the table incomplete as printed.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation: the three-family constraint is an imposed search condition and the beta-function survey reports failures as well as successes; the main issue is under-specification of hidden-brane fixed-point data, not circularity.

full rationale

No load-bearing step reduces to its own input. The three-family condition (2.24), Iab + Iab' = -(Iac + Iac' + Iad + Iad') = ±3, is imposed during the search and the models are selected to satisfy it; the paper does not claim to predict three families from an independent input, so this is standard model building rather than a fitted parameter renamed as a prediction. The asymptotic-freedom check (4.8) is reported for all ten models, including the six with positive beta coefficients, so there is no selection bias toward the advertised outcome. The rigid-brane spectrum rules, discrete-torsion consistency, and K-theory constraints are cited to external works ([25], [42], [44]-[47]), not to the present authors' prior results. The self-citations, including the companion letter [41], are pointers or contextual references and are not load-bearing for the construction. The central limitation is different: the fixed-point sets S^g_a and signs epsilon^g_a,ij required by (2.10), (2.30), and the intersection numbers (2.11)-(2.19) are not tabulated, and Section 3 explicitly relies on undisclosed displacements of hidden branes to 'alternative orbifold fixed points' to remove unwanted massless matter. This makes the twisted-tadpole cancellation and the detailed spectra not independently checkable from the manuscript as written. That is an under-specification/completeness gap, which affects verifiability and correctness risk, but it is not circularity: the missing data are inputs that would allow the reader to check the tabulated outputs, not outputs that are fed back into the derivation. Accordingly, the circularity score is low, reflecting only the presence of minor, non-load-bearing self-citations.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The hand-chosen inputs are the integer wrapping numbers and the discrete fixed-point and sign assignments, which form the search space of this model-building program rather than fitted data; the complex-structure moduli are solved from the SUSY conditions (2.28). The central unverified cost is the assumption that hidden-sector gauge dynamics confine and decouple the exotic states, asserted in the composite-spectrum tables without computing hidden beta functions. No new particles, forces, or dimensions are introduced.

free parameters (3)
  • Integer wrapping numbers of every D6-brane stack = listed per model in Appendix A (Tables 23-32)
    The brane configurations are hand-chosen to satisfy N=1 SUSY, tadpole cancellation, K-theory, and the three-family condition (2.24); they are the inputs of the construction, not quantities fitted to observational data.
  • Complex structure moduli chi_1, chi_2, chi_3 = model-dependent; e.g., r06: sqrt(13), 12/sqrt(13), 16/sqrt(13)
    Solved from the supersymmetry conditions (2.28) for each model and then used in the gauge coupling relations (2.41) and the appendix captions; not fitted to data.
  • Hidden-sector fixed-point displacement assignments (stacks e, f, g, ...) = not specified
    Section 3 asserts hidden branes are displaced to alternative orbifold fixed points so that unwanted intersection numbers vanish; the specific choices are not tabulated, yet the tabulated spectra depend on them.
assumptions (5)
  • domain assumption Standard intersecting-D6-brane spectrum, intersection, and tadpole formulas (Eqs. 2.6-2.23, 2.29-2.32, Table 2).
    The paper applies the standard technology of this orientifold without re-deriving it; developed primarily in refs [4,25,42].
  • domain assumption Discrete torsion eta = -1 consistency: an odd number of O6(+,+) planes is required (2.5).
    Inherited from ref. [25]; the whole construction assumes this constraint.
  • domain assumption Rigid fractional branes have no massless adjoint chiral multiplets.
    The central motivation; stated in Section 2 and following refs [25,42].
  • domain assumption Maximal gauge-group rank bound r(V) <= 138 for N=1 Pati-Salam models.
    External swampland result from ref. [36], invoked in Section 1 to claim the models satisfy the rank bound.
  • ad hoc to paper Hidden-sector gauge dynamics confine exotic states into the tabulated bound states, decoupling them at low energy.
    Load-bearing for the claim that models are phenomenologically viable; the composite-spectrum tables (e.g., Tables 6, 10, 12) assert the confined spectra but no hidden-sector beta functions or dynamics are computed.

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Pith. "Pith review of Three-family supersymmetric Pati-Salam models from intersecting D6-branes on rigid cycles." pith.science (2026). https://pith.science/paper/FJQFAPCE

@misc{pith2026250503664,
  author       = {Pith},
  title        = {Pith review of: Three-family supersymmetric Pati-Salam models from intersecting D6-branes on rigid cycles},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FJQFAPCE}},
  note         = {Machine review of arXiv:2505.03664}
}
abstract

Intersecting D6-brane models without discrete torsion typically suffer from unstabilized open string moduli, arising from D-brane positions and Wilson lines. These moduli generate additional massless adjoint fields, obstructing the realization of negative beta functions necessary for asymptotic freedom unless they are decoupled around string scale. A viable solution involves utilizing rigid cycles, which eliminate these unwanted adjoint fields. In this work, we for the first time present a class of consistent three-family supersymmetric Pati-Salam models from rigid intersecting D6-branes on the factorizable $\mathbb{T}^6/(\mathbb{Z}_2 \times \mathbb{Z}_2^\prime)$ orientifold with discrete torsion. These models satisfy all the known consistency conditions, including $\mathcal{N}=1$ supersymmetry, K-theory constraints, tadpole cancellation, and recent swampland bounds on the maximal gauge group rank. We provide detailed particle spectra, analyze their phenomenological implications, and discuss the decoupling of exotic states through strong dynamics in the hidden sector.

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Works this paper leans on

54 extracted references · 12 canonical work pages

  1. [1]

    Three-Family Supersymmetric Standard-like Models from Intersecting Brane Worlds

    M. Cvetic, 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]

    work page Pith review arXiv 2001

  2. [2]

    Cvetic, G

    M. Cvetic, 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]

    arXiv 2001

  3. [3]

    Supersymmetric Three Family SU(5) Grand Unified Models from Type IIA Orientifolds with Intersecting D6-Branes

    M. Cvetic, 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 [hep-th/0212177]

    work page Pith review arXiv 2003

  4. [4]

    Cvetic, T

    M. Cvetic, 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]

    arXiv 2004

  5. [5]

    Blumenhagen, M

    R. Blumenhagen, M. Cvetic, P. Langacker and G. Shiu, Toward realistic intersecting D-brane models, Ann. Rev. Nucl. Part. Sci. 55 (2005) 71 [ hep-th/0502005]

    arXiv 2005

  6. [6]

    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]

    arXiv 2006

  7. [7]

    C.-M. Chen, T. Li and D. V. Nanopoulos, Type IIA Pati-Salam flux vacua , Nucl. Phys. B 740 (2006) 79 [ hep-th/0601064]

    arXiv 2006

  8. [8]

    C.-M. Chen, T. Li and D. V. Nanopoulos, Flipped and unflipped SU(5) as type IIA flux vacua , Nucl. Phys. B 751 (2006) 260 [ hep-th/0604107]

    work page Pith review arXiv 2006

Show all 54 references
  1. [9]

    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]

    2008 arXiv

  2. [10]

    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 [0711.0396]

    2008 arXiv

  3. [11]

    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 (2022) 710 [ 2112.09630]

    2022 arXiv

  4. [12]

    W. He, T. Li and R. Sun, The complete search for the supersymmetric Pati-Salam models from intersecting D6-branes, JHEP 08 (2022) 044 [ 2112.09632]

    2022 arXiv

  5. [13]

    T. Li, R. Sun and L. Wu, String-scale gauge coupling relations in the supersymmetric Pati-Salam models from intersecting D6-branes , JHEP 03 (2023) 210 [ 2212.05875]

    2023 arXiv

  6. [14]

    Sabir, T

    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, JHEP 04 (2022) 089 [ 2202.07048]

    2022 arXiv

  7. [15]

    T. Li, A. Mansha and R. Sun, Revisiting the supersymmetric Pati–Salam models from intersecting D6-branes, Eur. Phys. J. C 81 (2021) 82 [ 1910.04530]

    2021 arXiv

  8. [16]

    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×SU (2)R models, and SU (4)C×SU (2)L×SU (6)R models from intersecting D6-branes, Phys. Rev. D 104 (2021) 046018

    2021

  9. [17]

    Mansha, T

    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 (2024) 151 [ 2212.09644]. – 40 –

    2024 arXiv

  10. [18]

    Mansha, T

    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 (2023) 1067 [2303.02864]

    2023 arXiv

  11. [19]

    Sabir, A

    M. Sabir, A. Mansha, T. Li and Z.-W. Wang, Fermion masses and mixings in the supersymmetric Pati-Salam landscape from Intersecting D6-Branes , JHEP 10 (2024) 252 [2409.09110]

    2024 arXiv

  12. [20]

    Sabir, A

    M. Sabir, A. Mansha, T. Li and Z.-W. Wang, Susy breaking soft terms in the supersymmetric Pati-Salam landscape from intersecting D6-branes , JHEP 01 (2025) 201 [ 2410.09093]

    2025 arXiv

  13. [21]

    Sabir, A

    M. Sabir, A. Mansha, T. Li and Z.-W. Wang, Fermion masses and mixings in string theory with Dirac neutrinos , Phys. Rev. D 111 (2025) L071702 [ 2407.19458]

    2025

  14. [22]

    Mansha, T

    A. Mansha, T. Li and M. Sabir, Revisiting the supersymmetric trinification models from intersecting D6-branes, Commun. Theor. Phys. 76 (2024) 095201 [ 2406.07586]

    2024 arXiv

  15. [23]

    Assel, K

    B. Assel, K. Christodoulides, A. E. Faraggi, C. Kounnas and J. Rizos, Classification of Heterotic Pati-Salam Models, Nucl. Phys. B 844 (2011) 365 [ 1007.2268]

    2011 arXiv

  16. [24]

    A. E. Faraggi, V. G. Matyas and B. Percival, Classification of nonsupersymmetric Pati-Salam heterotic string models, Phys. Rev. D 104 (2021) 046002 [ 2011.04113]

    2021 arXiv

  17. [25]

    Blumenhagen, M

    R. Blumenhagen, M. Cvetic, F. Marchesano and G. Shiu, Chiral D-brane models with frozen open string moduli, JHEP 03 (2005) 050 [ hep-th/0502095]

    2005 arXiv

  18. [26]

    Forste and I

    S. Forste and I. Zavala, Oddness from Rigidness, JHEP 07 (2008) 086 [ 0806.2328]

    2008 arXiv

  19. [27]

    Blumenhagen, V

    R. Blumenhagen, V. Braun, B. Kors and D. Lust, Orientifolds of K3 and Calabi-Yau manifolds with intersecting D-branes , JHEP 07 (2002) 026 [ hep-th/0206038]

    2002 arXiv

  20. [28]

    L. E. Ibanez and R. Richter, Stringy Instantons and Yukawa Couplings in MSSM-like Orientifold Models, JHEP 03 (2009) 090 [ 0811.1583]

    2009 arXiv

  21. [29]

    Blumenhagen, M

    R. Blumenhagen, M. Cvetic and T. Weigand, Spacetime instanton corrections in 4D string vacua: The Seesaw mechanism for D-Brane models , Nucl. Phys. B 771 (2007) 113 [hep-th/0609191]

    2007 arXiv

  22. [30]

    L. E. Ibanez and A. M. Uranga, Neutrino Majorana Masses from String Theory Instanton Effects, JHEP 03 (2007) 052 [ hep-th/0609213]

    2007 arXiv

  23. [31]

    S. A. Abel and M. D. Goodsell, Realistic Yukawa Couplings through Instantons in Intersecting Brane Worlds, JHEP 10 (2007) 034 [ hep-th/0612110]

    2007 arXiv

  24. [32]

    Blumenhagen, M

    R. Blumenhagen, M. Cvetic, D. Lust, R. Richter and T. Weigand, Non-perturbative Yukawa Couplings from String Instantons , Phys. Rev. Lett. 100 (2008) 061602 [ 0707.1871]

    2008 arXiv

  25. [33]

    T. D. Brennan, F. Carta and C. Vafa, The String Landscape, the Swampland, and the Missing Corner, PoS T ASI2017(2017) 015 [ 1711.00864]

    2017 arXiv

  26. [34]

    Kim, H.-C

    H.-C. Kim, H.-C. Tarazi and C. Vafa, Four-dimensionalN = 4 SYM theory and the swampland, Phys. Rev. D 102 (2020) 026003 [ 1912.06144]

    2020 arXiv

  27. [35]

    H.-C. Kim, C. Vafa and K. Xu, Finite Landscape of 6d N=(1,0) Supergravity , 2411.19155

  28. [36]

    G. J. Loges and G. Shiu, 134 billion intersecting brane models , JHEP 12 (2022) 097 [2206.03506]

    2022 arXiv

  29. [37]

    N. B. Agmon, A. Bedroya, M. J. Kang and C. Vafa, Lectures on the string landscape and the Swampland, 2212.06187. – 41 –

    arXiv

  30. [38]

    Palti, The Swampland: Introduction and Review , Fortsch

    E. Palti, The Swampland: Introduction and Review , Fortsch. Phys. 67 (2019) 1900037 [1903.06239]

    2019 arXiv

  31. [39]

    van Beest, J

    M. van Beest, J. Calder´ on-Infante, D. Mirfendereski and I. Valenzuela, Lectures on the Swampland Program in String Compactifications , Phys. Rept. 989 (2022) 1 [ 2102.01111]

    2022 arXiv

  32. [40]

    Van Riet and G

    T. Van Riet and G. Zoccarato, Beginners lectures on flux compactifications and related Swampland topics, Phys. Rept. 1049 (2024) 1 [ 2305.01722]

    2024 arXiv

  33. [41]

    Mansha, M

    A. Mansha, M. Sabir, T. Li and L. Wang, Three family supersymmetric Pati-Salam model from rigid intersecting D6-branes , Phys. Rev. D 111 (2025) L121904 [ 2501.08590]

    2025 arXiv

  34. [42]

    Forste and G

    S. Forste and G. Honecker, Rigid D6-branes on T 6/(Z2×Z2M× ΩR) with discrete torsion , JHEP 01 (2011) 091 [ 1010.6070]

    2011 arXiv

  35. [43]

    M. B. Green and J. H. Schwarz, Anomaly Cancellation in Supersymmetric D=10 Gauge Theory and Superstring Theory , Phys. Lett. B 149 (1984) 117

    1984

  36. [44]

    J. F. G. Cascales and A. M. Uranga, Chiral 4d string vacua with D branes and NSNS and RR fluxes, JHEP 05 (2003) 011 [ hep-th/0303024]

    2003 arXiv

  37. [45]

    Marchesano and G

    F. Marchesano and G. Shiu, MSSM vacua from flux compactifications , Phys. Rev. D 71 (2005) 011701 [hep-th/0408059]

    2005 arXiv

  38. [46]

    Marchesano and G

    F. Marchesano and G. Shiu, Building MSSM flux vacua , JHEP 11 (2004) 041 [hep-th/0409132]

    2004 arXiv

  39. [47]

    A. M. Uranga, D-brane probes, RR tadpole cancellation and K-theory charge , Nucl. Phys. B 598 (2001) 225 [ hep-th/0011048]

    2001 arXiv

  40. [48]

    Cvetic, P

    M. Cvetic, 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]

    2003 arXiv

  41. [49]

    D. Lust, P. Mayr, R. Richter and S. Stieberger, Scattering of gauge, matter, and moduli fields from intersecting branes, Nucl. Phys. B 696 (2004) 205 [ hep-th/0404134]

    2004 arXiv

  42. [50]

    Blumenhagen, B

    R. Blumenhagen, B. Kors, D. Lust and S. Stieberger, Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes , Phys. Rept. 445 (2007) 1 [hep-th/0610327]

    2007 arXiv

  43. [51]

    P. H. Ginsparg, Gauge and Gravitational Couplings in Four-Dimensional String Theories , Phys. Lett. B 197 (1987) 139

    1987

  44. [52]

    Hamada, T

    Y. Hamada, T. Kobayashi and S. Uemura, Standard Model-like D-brane models and gauge couplings, Nucl. Phys. B 897 (2015) 563 [ 1409.2740]

    2015 arXiv

  45. [53]

    K. R. Dienes and J. March-Russell, Realizing higher level gauge symmetries in string theory: New embeddings for string GUTs , Nucl. Phys. B 479 (1996) 113 [ hep-th/9604112]

    1996 arXiv

  46. [54]

    Ishiguro, S

    K. Ishiguro, S. Nishimura and H. Otsuka, Autoencoder-driven clustering of intersecting D-brane models via tadpole charge , JHEP 08 (2024) 133 [ 2312.07181]. – 42 –

    2024 arXiv

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