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Brane brick models and 2d (0, 2) triality

  • Sebastián Franco
  • Sangmin Lee
  • Rak-Kyeong Seong
Open Access
Regular Article - Theoretical Physics

Abstract

We provide a brane realization of 2d (0, 2) Gadde-Gukov-Putrov triality in terms of brane brick models. These are Type IIA brane configurations that are T-dual to D1-branes over singular toric Calabi-Yau 4-folds. Triality translates into a local transformation of brane brick models, whose simplest representative is a cube move. We present explicit examples and construct their triality networks. We also argue that the classical mesonic moduli space of brane brick model theories, which corresponds to the probed Calabi-Yau 4-fold, is invariant under triality. Finally, we discuss triality in terms of phase boundaries, which play a central role in connecting Calabi-Yau 4-folds to brane brick models.

Keywords

Brane Dynamics in Gauge Theories D-branes Supersymmetric gauge theory 

Notes

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.

References

  1. [1]
    F. Benini and N. Bobev, Exact two-dimensional superconformal R-symmetry and c-extremization, Phys. Rev. Lett. 110 (2013) 061601 [arXiv:1211.4030] [INSPIRE].CrossRefADSGoogle Scholar
  2. [2]
    F. Benini and N. Bobev, Two-dimensional SCFTs from wrapped branes and c-extremization, JHEP 06 (2013) 005 [arXiv:1302.4451] [INSPIRE].CrossRefADSGoogle Scholar
  3. [3]
    A. Gadde, S. Gukov and P. Putrov, Exact Solutions of 2d Supersymmetric Gauge Theories, arXiv:1404.5314 [INSPIRE].
  4. [4]
    A. Gadde, Holomorphy, triality and non-perturbative β-function in 2d supersymmetric QCD, arXiv:1506.07307 [INSPIRE].
  5. [5]
    D. Kutasov and J. Lin, (0,2) Dynamics From Four Dimensions, Phys. Rev. D 89 (2014) 085025 [arXiv:1310.6032] [INSPIRE].
  6. [6]
    D. Kutasov and J. Lin, (0,2) ADE Models From Four Dimensions, arXiv:1401.5558 [INSPIRE].
  7. [7]
    A. Gadde, S. Gukov and P. Putrov, Fivebranes and 4-manifolds, arXiv:1306.4320 [INSPIRE].
  8. [8]
    A. Gadde, S. Gukov and P. Putrov, (0, 2) trialities, JHEP 03 (2014) 076 [arXiv:1310.0818] [INSPIRE].
  9. [9]
    N. Seiberg, Electric-magnetic duality in supersymmetric nonAbelian gauge theories, Nucl. Phys. B 435 (1995) 129 [hep-th/9411149] [INSPIRE].MathSciNetCrossRefzbMATHADSGoogle Scholar
  10. [10]
    H. Garcia-Compean and A.M. Uranga, Brane box realization of chiral gauge theories in two-dimensions, Nucl. Phys. B 539 (1999) 329 [hep-th/9806177] [INSPIRE].MathSciNetCrossRefzbMATHADSGoogle Scholar
  11. [11]
    S. Franco, D. Ghim, S. Lee, R.-K. Seong and D. Yokoyama, 2d (0,2) Quiver Gauge Theories and D-branes, JHEP 09 (2015) 072 [arXiv:1506.03818] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  12. [12]
    R. Tatar, Geometric Constructions of Two Dimensional (0,2) SUSY Theories, Phys. Rev. D 92 (2015) 045006 [arXiv:1506.05372] [INSPIRE].MathSciNetADSGoogle Scholar
  13. [13]
    F. Benini, N. Bobev and P.M. Crichigno, Two-dimensional SCFTs from D3-branes, arXiv:1511.09462 [INSPIRE].
  14. [14]
    S. Schäfer-Nameki and T. Weigand, F-theory and 2d (0,2) Theories, arXiv:1601.02015 [INSPIRE].
  15. [15]
    S. Franco, S. Lee and R.-K. Seong, Brane Brick Models, Toric Calabi-Yau 4-Folds and 2d (0,2) Quivers, JHEP 02 (2016) 047 [arXiv:1510.01744] [INSPIRE].CrossRefADSGoogle Scholar
  16. [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].MathSciNetCrossRefzbMATHADSGoogle Scholar
  17. [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].MathSciNetCrossRefzbMATHADSGoogle Scholar
  18. [18]
    C.E. Beasley and M.R. Plesser, Toric duality is Seiberg duality, JHEP 12 (2001) 001 [hep-th/0109053] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  19. [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].MathSciNetCrossRefADSGoogle Scholar
  20. [20]
    E. Witten, Phases of N = 2 theories in two-dimensions, Nucl. Phys. B 403 (1993) 159 [hep-th/9301042] [INSPIRE].MathSciNetCrossRefzbMATHADSGoogle Scholar
  21. [21]
    M. Futaki and K. Ueda, Tropical coamoeba and torus-equivariant homological mirror symmetry for the projective space, [arXiv:1001.4858].
  22. [22]
    K. Mohri, D-branes and quotient singularities of Calabi-Yau fourfolds, Nucl. Phys. B 521 (1998) 161 [hep-th/9707012] [INSPIRE].MathSciNetCrossRefzbMATHADSGoogle Scholar
  23. [23]
    F. Benini, D.S. Park and P. Zhao, Cluster Algebras from Dualities of 2d \( \mathcal{N} = \left(2,\;2\right) \) Quiver Gauge Theories, Commun. Math. Phys. 340 (2015) 47 [arXiv:1406.2699] [INSPIRE].MathSciNetCrossRefzbMATHADSGoogle Scholar
  24. [24]
    B. Feng, S. Franco, A. Hanany and Y.-H. He, Symmetries of toric duality, JHEP 12 (2002) 076 [hep-th/0205144] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  25. [25]
    A. Hanany and D. Vegh, Quivers, tilings, branes and rhombi, JHEP 10 (2007) 029 [hep-th/0511063] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  26. [26]
    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].MathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    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].MathSciNetCrossRefADSGoogle Scholar
  28. [28]
    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].MathSciNetCrossRefADSGoogle Scholar
  29. [29]
    A.B. Goncharov and R. Kenyon, Dimers and cluster integrable systems, arXiv:1107.5588 [INSPIRE].
  30. [30]
    S. Franco, Dimer Models, Integrable Systems and Quantum Teichmüller Space, JHEP 09 (2011) 057 [arXiv:1105.1777] [INSPIRE].MathSciNetCrossRefzbMATHADSGoogle Scholar
  31. [31]
    R. Eager, S. Franco and K. Schaeffer, Dimer Models and Integrable Systems, JHEP 06 (2012) 106 [arXiv:1107.1244] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  32. [32]
    M. Yamazaki, Quivers, YBE and 3-manifolds, JHEP 05 (2012) 147 [arXiv:1203.5784] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  33. [33]
    S. Franco, D. Galloni and Y.-H. He, Towards the Continuous Limit of Cluster Integrable Systems, JHEP 09 (2012) 020 [arXiv:1203.6067] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  34. [34]
    M. Yamazaki and W. Yan, Integrability from 2d \( \mathcal{N} = \left(2,2\right) \) dualities, J. Phys. A 48 (2015) 394001 [arXiv:1504.05540] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  35. [35]
    S. Franco, Y. Hatsuda and M. Mariño, Exact quantization conditions for cluster integrable systems, arXiv:1512.03061 [INSPIRE].
  36. [36]
    A.B. Zamolodchikov, Tetrahedron Equations and the Relativistic S Matrix of Straight Strings in (2+1)-dimensions, Commun. Math. Phys. 79 (1981) 489 [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  37. [37]
    A. Gadde, S. Gukov and P. Putrov, Walls, Lines and Spectral Dualities in 3d Gauge Theories, JHEP 05 (2014) 047 [arXiv:1302.0015] [INSPIRE].CrossRefADSGoogle Scholar
  38. [38]
    A. Gadde and S. Gukov, 2d Index and Surface operators, JHEP 03 (2014) 080 [arXiv:1305.0266] [INSPIRE].MathSciNetCrossRefzbMATHADSGoogle Scholar
  39. [39]
    F. Benini, R. Eager, K. Hori and Y. Tachikawa, Elliptic genera of two-dimensional N = 2 gauge theories with rank-one gauge groups, Lett. Math. Phys. 104 (2014) 465 [arXiv:1305.0533] [INSPIRE].MathSciNetCrossRefzbMATHADSGoogle Scholar
  40. [40]
    F. Benini, R. Eager, K. Hori and Y. Tachikawa, Elliptic Genera of 2d \( \mathcal{N}=2 \) Gauge Theories, Commun. Math. Phys. 333 (2015) 1241 [arXiv:1308.4896] [INSPIRE].MathSciNetCrossRefzbMATHADSGoogle Scholar
  41. [41]
    S.H. Katz and E. Sharpe, Notes on certain (0,2) correlation functions, Commun. Math. Phys. 262 (2006) 611 [hep-th/0406226] [INSPIRE].MathSciNetCrossRefzbMATHADSGoogle Scholar
  42. [42]
    R. Donagi, J. Guffin, S. Katz and E. Sharpe, A Mathematical Theory of Quantum Sheaf Cohomology, Asian J. Math. 18 (2014) 387 [arXiv:1110.3751] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  43. [43]
    R. Donagi, J. Guffin, S. Katz and E. Sharpe, Physical aspects of quantum sheaf cohomology for deformations of tangent bundles of toric varieties, Adv. Theor. Math. Phys. 17 (2013) 1255 [arXiv:1110.3752] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  44. [44]
    J. Guo, B. Jia and E. Sharpe, Chiral operators in two-dimensional (0,2) theories and a test of triality, JHEP 06 (2015) 201 [arXiv:1501.00987] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  45. [45]
    A. Adams, J. Distler and M. Ernebjerg, Topological heterotic rings, Adv. Theor. Math. Phys. 10 (2006) 657 [hep-th/0506263] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  46. [46]
    S. Franco, D. Ghim, S. Lee and R.-K. Seong, to appear.Google Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Sebastián Franco
    • 1
    • 2
  • Sangmin Lee
    • 3
    • 4
    • 5
    • 6
  • Rak-Kyeong Seong
    • 7
  1. 1.Physics DepartmentThe City College of the CUNYNew YorkU.S.A.
  2. 2.The Graduate School and University CenterThe City University of New YorkNew YorkU.S.A.
  3. 3.Center for Theoretical PhysicsSeoul National UniversitySeoulKorea
  4. 4.Department of Physics and AstronomySeoul National UniversitySeoulKorea
  5. 5.College of Liberal StudiesSeoul National UniversitySeoulKorea
  6. 6.School of Natural SciencesInstitute for Advanced StudyPrincetonU.S.A.
  7. 7.School of PhysicsKorea Institute for Advanced StudySeoulKorea

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