Quadrality for supersymmetric matrix models

Abstract

We introduce a new duality for \( \mathcal{N} \) = 1 supersymmetric gauged matrix models. This 0d duality is an order 4 symmetry, namely an equivalence between four different theories, hence we call it Quadrality. Our proposal is motivated by mirror symmetry, but is not restricted to theories with a D-brane realization and holds for general \( \mathcal{N} \) = 1 matrix models. We present various checks of the proposal, including the matching of: global symmetries, anomalies, deformations and the chiral ring. We also consider quivers and the corresponding quadrality networks. Finally, we initiate the study of matrix models that arise on the worldvolume of D(-1)-branes probing toric Calabi-Yau 5-folds.

A preprint version of the article is available at ArXiv.

References

  1. [1]

    N. Seiberg, Electric-magnetic duality in supersymmetric nonAbelian gauge theories, Nucl. Phys. B 435 (1995) 129 [hep-th/9411149] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  2. [2]

    A. Gadde, S. Gukov and P. Putrov, (0, 2) trialities, JHEP 03 (2014) 076 [arXiv:1310.0818] [INSPIRE].

  3. [3]

    S. Franco, S. Lee, R.-K. Seong and C. Vafa, Brane brick models in the mirror, JHEP 02 (2017) 106 [arXiv:1609.01723] [INSPIRE].

    ADS  Article  Google Scholar 

  4. [4]

    F. Cachazo, B. Fiol, K.A. Intriligator, S. Katz and C. Vafa, A geometric unification of dualities, Nucl. Phys. B 628 (2002) 3 [hep-th/0110028] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  5. [5]

    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].

    MathSciNet  Google Scholar 

  6. [6]

    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  Article  Google Scholar 

  7. [7]

    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  Article  Google Scholar 

  8. [8]

    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].

    ADS  MathSciNet  Article  Google Scholar 

  9. [9]

    S. Franco, S. Lee and R.-K. Seong, Brane brick models and 2d (0, 2) triality, JHEP 05 (2016) 020 [arXiv:1602.01834] [INSPIRE].

    ADS  Article  Google Scholar 

  10. [10]

    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  Article  MATH  Google Scholar 

  11. [11]

    M. Futaki and K. Ueda, Tropical Coamoeba and torus-equivariant homological mirror symmetry for the projective space, Commun. Math. Phys. 332 (2014) 53 [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  12. [12]

    K. Hori and C. Vafa, Mirror symmetry, hep-th/0002222 [INSPIRE].

  13. [13]

    K. Hori, A. Iqbal and C. Vafa, D-branes and mirror symmetry, hep-th/0005247 [INSPIRE].

  14. [14]

    S. Franco, A. Hanany, Y.-H. He and P. Kazakopoulos, Duality walls, duality trees and fractional branes, hep-th/0306092 [INSPIRE].

  15. [15]

    S. Franco, Y.-H. He, C. Herzog and J. Walcher, Chaotic duality in string theory, Phys. Rev. D 70 (2004) 046006 [hep-th/0402120] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  16. [16]

    N. Ishibashi, H. Kawai, Y. Kitazawa and A. Tsuchiya, A large-N reduced model as superstring, Nucl. Phys. B 498 (1997) 467 [hep-th/9612115] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  17. [17]

    M. Fukuma, H. Kawai, Y. Kitazawa and A. Tsuchiya, String field theory from IIB matrix model, Nucl. Phys. B 510 (1998) 158 [hep-th/9705128] [INSPIRE].

    MathSciNet  Article  MATH  Google Scholar 

  18. [18]

    H. Aoki, S. Iso, H. Kawai, Y. Kitazawa and T. Tada, Space-time structures from IIB matrix model, Prog. Theor. Phys. 99 (1998) 713 [hep-th/9802085] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  19. [19]

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

  20. [20]

    M.R. Douglas, B.R. Greene and D.R. Morrison, Orbifold resolution by D-branes, Nucl. Phys. B 506 (1997) 84 [hep-th/9704151] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  21. [21]

    O. Aharony, S.S. Razamat, N. Seiberg and B. Willett, 3d dualities from 4d dualities, JHEP 07 (2013) 149 [arXiv:1305.3924] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  22. [22]

    O. Aharony, S.S. Razamat, N. Seiberg and B. Willett, 3d dualities from 4d dualities for orthogonal groups, JHEP 08 (2013) 099 [arXiv:1307.0511] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  23. [23]

    M. Honda and Y. Yoshida, Supersymmetric index on T 2 × S 2 and elliptic genus, arXiv:1504.04355 [INSPIRE].

  24. [24]

    A. Gadde, S.S. Razamat and B. Willett, On the reduction of 4d \( \mathcal{N} \) = 1 theories on \( {\mathbb{S}}^2 \), JHEP 11 (2015) 163 [arXiv:1506.08795] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  25. [25]

    Y. Imamura, Relation between the 4d superconformal index and the S 3 partition function, JHEP 09 (2011) 133 [arXiv:1104.4482] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  26. [26]

    A. Gadde and W. Yan, Reducing the 4d index to the S 3 partition function, JHEP 12 (2012) 003 [arXiv:1104.2592] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  27. [27]

    F.A.H. Dolan, V.P. Spiridonov and G.S. Vartanov, From 4d superconformal indices to 3d partition functions, Phys. Lett. B 704 (2011) 234 [arXiv:1104.1787] [INSPIRE].

    ADS  Article  Google Scholar 

  28. [28]

    F. Benini and B. Le Floch, Supersymmetric localization in two dimensions, arXiv:1608.02955 [INSPIRE].

  29. [29]

    A. Gadde, S. Gukov and P. Putrov, Exact solutions of 2d supersymmetric gauge theories, arXiv:1404.5314 [INSPIRE].

  30. [30]

    M.B. Green and M. Gutperle, D instanton partition functions, Phys. Rev. D 58 (1998) 046007 [hep-th/9804123] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  31. [31]

    S. Benvenuti, B. Feng, A. Hanany and Y.-H. He, Counting BPS operators in gauge theories: quivers, syzygies and plethystics, JHEP 11 (2007) 050 [hep-th/0608050] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  32. [32]

    B. Feng, A. Hanany and Y.-H. He, Counting gauge invariants: the plethystic program, JHEP 03 (2007) 090 [hep-th/0701063] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  33. [33]

    D. Martelli, J. Sparks and S.-T. Yau, Sasaki-Einstein manifolds and volume minimisation, Commun. Math. Phys. 280 (2008) 611 [hep-th/0603021] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  34. [34]

    O. Aharony and A. Hanany, Branes, superpotentials and superconformal fixed points, Nucl. Phys. B 504 (1997) 239 [hep-th/9704170] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  35. [35]

    O. Aharony, A. Hanany and B. Kol, Webs of (p, q) five-branes, five-dimensional field theories and grid diagrams, JHEP 01 (1998) 002 [hep-th/9710116] [INSPIRE].

    ADS  Article  Google Scholar 

  36. [36]

    N.C. Leung and C. Vafa, Branes and toric geometry, Adv. Theor. Math. Phys. 2 (1998) 91 [hep-th/9711013] [INSPIRE].

    MathSciNet  Article  MATH  Google Scholar 

  37. [37]

    A. Hanany and R.-K. Seong, Brane tilings and reflexive polygons, Fortsch. Phys. 60 (2012) 695 [arXiv:1201.2614] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

Download references

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.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Rak-Kyeong Seong.

Additional information

ArXiv ePrint: 1612.06859

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Franco, S., Lee, S., Seong, R. et al. Quadrality for supersymmetric matrix models. J. High Energ. Phys. 2017, 53 (2017). https://doi.org/10.1007/JHEP07(2017)053

Download citation

Keywords

  • Brane Dynamics in Gauge Theories
  • D-branes
  • Supersymmetric Gauge Theory