Skip to main content
Download PDF

Dimers, orientifolds and anomalies

Journal of High Energy Physics volume 2021, Article number: 153 (2021) Cite this article

A preprint version of the article is available at arXiv.

Abstract

We study 4d \( \mathcal{N} \) = 1 gauge theories engineered via D-branes at orientifolds of toric singularities, where gauge anomalies are cancelled without the introduction of non-compact flavor branes. Using dimer model techniques, we derive geometric criteria for establishing whether a given singularity can admit anomaly-free D-brane configurations purely based on its toric data and the type of orientifold projection. Our results therefore extend the dictionary between geometric properties of singularities and physical properties of the corresponding gauge theories.

References

  1. I. R. Klebanov and E. Witten, Superconformal field theory on three-branes at a Calabi-Yau singularity, Nucl. Phys. B 536 (1998) 199 [hep-th/9807080] [INSPIRE].

    ADS  MATH  Google Scholar 

  2. I. R. Klebanov and N. A. Nekrasov, Gravity duals of fractional branes and logarithmic RG flow, Nucl. Phys. B 574 (2000) 263 [hep-th/9911096] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  3. I. R. Klebanov and A. A. Tseytlin, Gravity duals of supersymmetric SU(N) × SU(N + M) gauge theories, Nucl. Phys. B 578 (2000) 123 [hep-th/0002159] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  4. I. R. Klebanov and M. J. Strassler, Supergravity and a confining gauge theory: Duality cascades and χSB-resolution of naked singularities, JHEP 08 (2000) 052 [hep-th/0007191] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  5. J. P. Gauntlett, D. Martelli, J. Sparks and D. Waldram, Sasaki-Einstein metrics on S2 × S3, Adv. Theor. Math. Phys. 8 (2004) 711 [hep-th/0403002] [INSPIRE].

    MathSciNet  MATH  Google Scholar 

  6. M. Bertolini, F. Bigazzi and A. L. Cotrone, New checks and subtleties for AdS/CFT and a-maximization, JHEP 12 (2004) 024 [hep-th/0411249] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  7. S. Benvenuti, S. Franco, A. Hanany, D. Martelli and J. Sparks, An Infinite family of superconformal quiver gauge theories with Sasaki-Einstein duals, JHEP 06 (2005) 064 [hep-th/0411264] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  8. M. Cvetič, H. Lü, D. N. Page and C. N. Pope, New Einstein-Sasaki spaces in five and higher dimensions, Phys. Rev. Lett. 95 (2005) 071101 [hep-th/0504225] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  9. S. Franco, A. Hanany, D. Martelli, J. Sparks, D. Vegh and B. Wecht, Gauge theories from toric geometry and brane tilings, JHEP 01 (2006) 128 [hep-th/0505211] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  10. A. Butti, D. Forcella and A. Zaffaroni, The Dual superconformal theory for Lp,q,r manifolds, JHEP 09 (2005) 018 [hep-th/0505220] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  11. 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].

    ADS  MathSciNet  MATH  Google Scholar 

  12. D. Berenstein, V. Jejjala and R. G. Leigh, The Standard model on a D-brane, Phys. Rev. Lett. 88 (2002) 071602 [hep-ph/0105042] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  13. H. Verlinde and M. Wijnholt, Building the standard model on a D3-brane, JHEP 01 (2007) 106 [hep-th/0508089] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  14. M. Buican, D. Malyshev, D. R. Morrison, H. Verlinde and M. Wijnholt, D-branes at Singularities, Compactification, and Hypercharge, JHEP 01 (2007) 107 [hep-th/0610007] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  15. D. Malyshev and H. Verlinde, D-branes at singularities and string phenomenology, Nucl. Phys. B Proc. Suppl. 171 (2007) 139 [arXiv:0711.2451] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  16. B. Feng, A. Hanany and Y.-H. He, D-brane gauge theories from toric singularities and toric duality, Nucl. Phys. B 595 (2001) 165 [hep-th/0003085] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  17. B. Feng, A. Hanany and Y.-H. He, Phase structure of D-brane gauge theories and toric duality, JHEP 08 (2001) 040 [hep-th/0104259] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  18. C. E. Beasley and M. R. Plesser, Toric duality is Seiberg duality, JHEP 12 (2001) 001 [hep-th/0109053] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  19. B. Feng, A. Hanany, Y.-H. He and A. M. Uranga, Toric duality as Seiberg duality and brane diamonds, JHEP 12 (2001) 035 [hep-th/0109063] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  20. B. Feng, S. Franco, A. Hanany and Y.-H. He, Symmetries of toric duality, JHEP 12 (2002) 076 [hep-th/0205144] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  21. D. Berenstein and M. R. Douglas, Seiberg duality for quiver gauge theories, hep-th/0207027 [INSPIRE].

  22. A. Hanany and K. D. Kennaway, Dimer models and toric diagrams, hep-th/0503149 [INSPIRE].

  23. S. Franco, A. Hanany, K. D. Kennaway, D. Vegh and B. Wecht, Brane dimers and quiver gauge theories, JHEP 01 (2006) 096 [hep-th/0504110] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  24. A. Sagnotti, Open Strings and their Symmetry Groups, in NATO Advanced Summer Institute on Nonperturbative Quantum Field Theory (Cargese Summer Institute), pp. 0521–528 (1987) [hep-th/0208020] [INSPIRE].

  25. G. Pradisi and A. Sagnotti, Open String Orbifolds, Phys. Lett. B 216 (1989) 59 [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  26. P. Hořava, Strings on World Sheet Orbifolds, Nucl. Phys. B 327 (1989) 461 [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  27. J. Dai, R. G. Leigh and J. Polchinski, New Connections Between String Theories, Mod. Phys. Lett. A 4 (1989) 2073 [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  28. M. Bianchi and A. Sagnotti, On the systematics of open string theories, Phys. Lett. B 247 (1990) 517 [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  29. M. Bianchi and A. Sagnotti, Twist symmetry and open string Wilson lines, Nucl. Phys. B 361 (1991) 519 [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  30. E. G. Gimon and J. Polchinski, Consistency conditions for orientifolds and d manifolds, Phys. Rev. D 54 (1996) 1667 [hep-th/9601038] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  31. M. R. Douglas and G. W. Moore, D-branes, quivers, and ALE instantons, hep-th/9603167 [INSPIRE].

  32. S. Franco, A. Hanany, D. Krefl, J. Park, A. M. Uranga and D. Vegh, Dimers and orientifolds, JHEP 09 (2007) 075 [arXiv:0707.0298] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  33. R. Argurio and M. Bertolini, Orientifolds and duality cascades: confinement before the wall, JHEP 02 (2018) 149 [arXiv:1711.08983] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  34. R. Argurio, M. Bertolini, G. Ferretti, A. Lerda and C. Petersson, Stringy instantons at orbifold singularities, JHEP 06 (2007) 067 [arXiv:0704.0262] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  35. M. Bianchi, F. Fucito and J. F. Morales, D-brane instantons on the T6/Z3 orientifold, JHEP 07 (2007) 038 [arXiv:0704.0784] [INSPIRE].

    ADS  Google Scholar 

  36. R. Blumenhagen, M. Cvetič, S. Kachru and T. Weigand, D-Brane Instantons in Type II Orientifolds, Ann. Rev. Nucl. Part. Sci. 59 (2009) 269 [arXiv:0902.3251] [INSPIRE].

    ADS  Google Scholar 

  37. R. Argurio, M. Bertolini, S. Franco and S. Kachru, Meta-stable vacua and D-branes at the conifold, JHEP 06 (2007) 017 [hep-th/0703236] [INSPIRE].

    ADS  MATH  Google Scholar 

  38. D. Berenstein, C. P. Herzog, P. Ouyang and S. Pinansky, Supersymmetry breaking from a Calabi-Yau singularity, JHEP 09 (2005) 084 [hep-th/0505029] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  39. S. Franco, A. Hanany, F. Saad and A. M. Uranga, Fractional branes and dynamical supersymmetry breaking, JHEP 01 (2006) 011 [hep-th/0505040] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  40. M. Bertolini, F. Bigazzi and A. L. Cotrone, Supersymmetry breaking at the end of a cascade of Seiberg dualities, Phys. Rev. D 72 (2005) 061902 [hep-th/0505055] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  41. G. Buratti, E. García-Valdecasas and A. M. Uranga, Supersymmetry Breaking Warped Throats and the Weak Gravity Conjecture, JHEP 04 (2019) 111 [arXiv:1810.07673] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  42. R. Argurio, M. Bertolini, S. Meynet and A. Pasternak, On supersymmetry breaking vacua from D-branes at orientifold singularities, JHEP 12 (2019) 145 [arXiv:1909.04682] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  43. R. G. Leigh and M. Rozali, Brane boxes, anomalies, bending and tadpoles, Phys. Rev. D 59 (1999) 026004 [hep-th/9807082] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  44. M. Bianchi and J. F. Morales, Anomalies & tadpoles, JHEP 03 (2000) 030 [hep-th/0002149] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  45. M. Bianchi, G. Inverso, J. F. Morales and D. Ricci Pacifici, Unoriented Quivers with Flavour, JHEP 01 (2014) 128 [arXiv:1307.0466] [INSPIRE].

    ADS  Google Scholar 

  46. S. Franco, A. Retolaza and A. Uranga, D-brane Instantons as Gauge Instantons in Orientifolds of Chiral Quiver Theories, JHEP 11 (2015) 165 [arXiv:1507.05330] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  47. J. Park, R. Rabadán and A. M. Uranga, Orientifolding the conifold, Nucl. Phys. B 570 (2000) 38 [hep-th/9907086] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  48. M. Bianchi, D. Bufalini, S. Mancani and F. Riccioni, Mass deformations of unoriented quiver theories, JHEP 07 (2020) 015 [arXiv:2003.09620] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  49. A. Hanany and D. Vegh, Quivers, tilings, branes and rhombi, JHEP 10 (2007) 029 [hep-th/0511063] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  50. B. Feng, Y.-H. He, K. D. Kennaway and C. Vafa, Dimer models from mirror symmetry and quivering amoebae, Adv. Theor. Math. Phys. 12 (2008) 489 [hep-th/0511287] [INSPIRE].

    MathSciNet  MATH  Google Scholar 

  51. S. Franco and D. Vegh, Moduli spaces of gauge theories from dimer models: Proof of the correspondence, JHEP 11 (2006) 054 [hep-th/0601063] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  52. D.-E. Diaconescu, M. R. Douglas and J. Gomis, Fractional branes and wrapped branes, JHEP 02 (1998) 013 [hep-th/9712230] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  53. A. Butti, Deformations of Toric Singularities and Fractional Branes, JHEP 10 (2006) 080 [hep-th/0603253] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

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

    ADS  MathSciNet  MATH  Google Scholar 

  55. L. E. Ibáñez, R. Rabadán and A. M. Uranga, Anomalous U(1)’s in type-I and type IIB D = 4, N = 1 string vacua, Nucl. Phys. B 542 (1999) 112 [hep-th/9808139] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  56. S. Benvenuti, A. Hanany and P. Kazakopoulos, The Toric phases of the Yp,q quivers, JHEP 07 (2005) 021 [hep-th/0412279] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  57. A. Butti and A. Zaffaroni, From toric geometry to quiver gauge theory: The Equivalence of a-maximization and Z-minimization, Fortsch. Phys. 54 (2006) 309 [hep-th/0512240] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  58. J. S. Scott, Grassmannians and cluster algebras, Proc. Lond. Math. Soc. 92 (2006) 345.

    MathSciNet  MATH  Google Scholar 

  59. A. B. Goncharov and R. Kenyon, Dimers and cluster integrable systems, Annales Sci. École Norm. Sup. 46 (2013) 747 arXiv:1107.5588 [INSPIRE].

  60. V.V. Fock, Inverse spectral problem for GK integrable system, arXiv:1503.00289.

  61. B. Feng, S. Franco, A. Hanany and Y.-H. He, UnHiggsing the del Pezzo, JHEP 08 (2003) 058 [hep-th/0209228] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  62. Y. Imamura, K. Kimura and M. Yamazaki, Anomalies and O-plane charges in orientifolded brane tilings, JHEP 03 (2008) 058 [arXiv:0801.3528] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  63. I. García-Etxebarria and B. Heidenreich, Strongly coupled phases of \( \mathcal{N} \) = 1 S-duality, JHEP 09 (2015) 032 [arXiv:1506.03090] [INSPIRE].

    MathSciNet  MATH  Google Scholar 

  64. I. García-Etxebarria and B. Heidenreich, S-duality in \( \mathcal{N} \) = 1 orientifold SCFTs, Fortsch. Phys. 65 (2017) 1700013 [arXiv:1612.00853] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  65. A. Retolaza and A. Uranga, Orientifolds of Warped Throats from Toric Calabi-Yau Singularities, JHEP 07 (2016) 135 [arXiv:1605.01732] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  66. M. Yamazaki, Brane Tilings and Their Applications, Fortsch. Phys. 56 (2008) 555 [arXiv:0803.4474] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  67. R. Argurio et al., The Octagon and the Non-Supersymmetric String Landscape, arXiv:2005.09671 [INSPIRE].

  68. R. Argurio et al., Dimers, Orientifolds and Stability of Supersymmetry Breaking Vacua, JHEP 01 (2021) 061 [arXiv:2007.13762] [INSPIRE].

    ADS  MATH  Google Scholar 

  69. M. Bianchi, S. Cremonesi, A. Hanany, J. F. Morales, D. Ricci Pacifici and R.-K. Seong, Mass-deformed Brane Tilings, JHEP 10 (2014) 027 [arXiv:1408.1957] [INSPIRE].

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physique Théorique et Mathématique and International Solvay Institutes, Université Libre de Bruxelles, C.P. 231, 1050, Brussels, Belgium

    Riccardo Argurio, Eduardo García-Valdecasas & Antoine Pasternak

  2. SISSA and INFN, Via Bonomea 265, I 34136, Trieste, Italy

    Matteo Bertolini & Shani Meynet

  3. Physics Department, The City College of the CUNY, 160 Convent Avenue, New York, NY, 10031, USA

    Sebastián Franco

  4. Physics Program and Initiative for the Theoretical Sciences, The Graduate School and University Center, The City University of New York, 365 Fifth Avenue, New York, NY, 10016, USA

    Sebastián Franco

  5. IRMA, UMR 7501, Université de Strasbourg et CNRS, 7 rue René Descartes, 67000, Strasbourg, France

    Valdo Tatitscheff

Authors
  1. Riccardo Argurio
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Matteo Bertolini
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sebastián Franco
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Eduardo García-Valdecasas
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Shani Meynet
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Antoine Pasternak
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Valdo Tatitscheff
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Eduardo García-Valdecasas.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

ArXiv ePrint: 2009.11291

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.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Argurio, R., Bertolini, M., Franco, S. et al. Dimers, orientifolds and anomalies. J. High Energ. Phys. 2021, 153 (2021). https://doi.org/10.1007/JHEP02(2021)153

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP02(2021)153

Keywords

  • Brane Dynamics in Gauge Theories
  • Gauge-gravity correspondence
  • Anomalies in Field and String Theories
  • Differential and Algebraic Geometry