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Quantum moduli space of Chern-Simons quivers, wrapped D6-branes and AdS 4 /CFT 3

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Abstract

We study the quantum moduli space of \( \mathcal{N} = 2 \) Chern-Simons quivers with generic ranks and CS levels, proving along the way exact formulas for the charges of bare monopole operators. We then derive \( \mathcal{N} = 2 \) Chern-Simons quiver theories dual to \( Ad{S_4} \times {Y^{p,q}}\left( {\mathbb{C}{\mathbb{P}^2}} \right) \) M-theory backgrounds, for the whole family of Sasaki-Einstein seven-manifolds and for any value of the torsion G 4 flux. The derivation of the gauge theories relies on the reduction to type IIA string theory, in which M2-branes become D2-branes while the conical geometry maps to RR flux and D6-branes wrapped on compact four-cycles. M5-branes on torsion cycles map to flux and wrapped D4-branes. The moduli space of the quiver is shown to contain the corresponding CY4 cone and all its crepant resolutions.

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References

  1. J. Bagger and N. Lambert, Modeling multiple M2’s, Phys. Rev. D 75 (2007) 045020 [hep-th/0611108] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  2. A. Gustavsson, Algebraic structures on parallel M2-branes, Nucl. Phys. B 811 (2009) 66 [arXiv:0709.1260] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  3. J. Bagger and N. Lambert, Gauge symmetry and supersymmetry of multiple M2-branes, Phys. Rev. D 77 (2008) 065008 [arXiv:0711.0955] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  4. O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, \( \mathcal{N} = 6 \) superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  5. M. Benna, I. Klebanov, T. Klose and M. Smedback, Superconformal Chern-Simons theories and AdS 4 /CFT 3 correspondence, JHEP 09 (2008) 072 [arXiv:0806.1519] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  6. Y. Imamura and K. Kimura, On the moduli space of elliptic Maxwell-Chern-Simons theories, Prog. Theor. Phys. 120 (2008) 509 [arXiv:0806.3727] [SPIRES].

    Article  MATH  ADS  Google Scholar 

  7. O. Aharony, O. Bergman and D.L. Jafferis, Fractional M2-branes, JHEP 11 (2008) 043 [arXiv:0807.4924] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  8. D.L. Jafferis and A. Tomasiello, A simple class of \( \mathcal{N} = 3 \) gauge/gravity duals, JHEP 10 (2008) 101 [arXiv:0808.0864] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  9. A. Hanany and A. Zaffaroni, Tilings, Chern-Simons theories and M2 branes, JHEP 10 (2008) 111 [arXiv:0808.1244] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  10. A. Hanany, D. Vegh and A. Zaffaroni, Brane tilings and M2 branes, JHEP 03 (2009) 012 [arXiv:0809.1440] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  11. I. Klebanov, T. Klose and A. Murugan, AdS 4 /CFT 3 — squashed, stretched and warped, JHEP 03 (2009) 140 [arXiv:0809.3773] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  12. M. Aganagic, A stringy origin of M2 brane Chern-Simons theories, Nucl. Phys. B 835 (2010) 1 [arXiv:0905.3415] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  13. D. Martelli and J. Sparks, AdS 4 /CFT 3 duals from M 2-branes at hypersurface singularities and their deformations, JHEP 12 (2009) 017 [arXiv:0909.2036] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  14. A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152 [hep-th/9611230] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  15. Y. Imamura and S. Yokoyama, \( \mathcal{N} = 4 \) Chern-Simons theories and wrapped M-branes in their gravity duals, Prog. Theor. Phys. 121 (2009) 915 [arXiv:0812.1331] [SPIRES].

    Article  MATH  ADS  Google Scholar 

  16. D. Gaiotto and D.L. Jafferis, Notes on adding D 6 branes wrapping RP3 in AdS 4× CP 3, arXiv:0903.2175 [SPIRES].

  17. S. Hohenegger and I. Kirsch, A note on the holography of Chern-Simons matter theories with flavour, JHEP 04 (2009) 129 [arXiv:0903.1730] [SPIRES].

    Article  ADS  Google Scholar 

  18. Y. Hikida, W. Li and T. Takayanagi, ABJM with flavors and FQHE, JHEP 07 (2009) 065 [arXiv:0903.2194] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  19. F. Benini, C. Closset and S. Cremonesi, Chiral flavors and M 2-branes at toric CY 4 singularities, JHEP 02 (2010) 036 [arXiv:0911.4127] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  20. D.L. Jafferis, Quantum corrections to \( \mathcal{N} = 2 \) Chern-Simons theories with flavor and their AdS4 duals, arXiv: 0911.4324 [SPIRES].

  21. J.P. Gauntlett, D. Martelli, J.F. Sparks and D. Waldram, A new infinite class of Sasaki-Einstein manifolds, Adv. Theor. Math. Phys. 8 (2006) 987 [hep-th/0403038] [SPIRES].

    MathSciNet  Google Scholar 

  22. D. Martelli and J. Sparks, Notes on toric Sasaki-Einstein seven-manifolds and AdS 4 /CFT 3 , JHEP 11 (2008) 016 [arXiv:0808.0904] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  23. F. Benini, C. Closset and S. Cremonesi, D 6-branes wrapped on toric del Pezzo surfaces and AdS 4 /CFT 3, to appear.

  24. D. Martelli and J. Sparks, Moduli spaces of Chern-Simons quiver gauge theories and AdS 4 /CFT 3, Phys. Rev. D 78 (2008) 126005 [arXiv:0808.0912] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  25. N. Benishti, Y.-H. He and J. Sparks, (Un)Higgsing the M2-brane, JHEP 01 (2010) 067 [arXiv:0909.4557] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  26. A. Kapustin, Wilson-’t Hooft operators in four-dimensional gauge theories and S-duality, Phys. Rev. D 74 (2006) 025005 [hep-th/0501015] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  27. A. Kapustin and E. Witten, Electric-magnetic duality and the geometric Langlands program, hep-th/0604151 [SPIRES].

  28. V. Borokhov, A. Kapustin and X.-k. Wu, Topological disorder operators in three-dimensional conformal field theory, JHEP 11 (2002) 049 [hep-th/0206054] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  29. V. Borokhov, A. Kapustin and X.-k. Wu, Monopole operators and mirror symmetry in three dimensions, JHEP 12 (2002) 044 [hep-th/0207074] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  30. V. Borokhov, Monopole operators in three-dimensional \( \mathcal{N} = 4 \) SYM and mirror symmetry, JHEP 03 (2004) 008 [hep-th/0310254] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  31. S. Kim, The complete superconformal index for XXX Chern-Simons theory, Nucl. Phys. B 821 (2009) 241 [arXiv:0903.4172] [SPIRES].

    Article  ADS  Google Scholar 

  32. M.K. Benna, I.R. Klebanov and T. Klose, Charges of monopole operators in Chern-Simons Yang-Mills theory, JHEP 01 (2010) 110 [arXiv:0906.3008] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  33. D. Bashkirov and A. Kapustin, Supersymmetry enhancement by monopole operators, JHEP 05 (2011) 015 [arXiv:1007.4861] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  34. H. Samtleben and R. Wimmer, XXX superspace constraints, SUSY enhancement and monopole operators, JHEP 10 (2010) 080 [arXiv:1008.2739] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  35. D.L. Jafferis, The exact superconformal R-symmetry extremizes Z, arXiv:1012.3210 [SPIRES].

  36. D. Gaiotto and E. Witten, S-duality of boundary conditions in \( \mathcal{N} = 4 \) super Yang-Mills theory, arXiv:0807.3720 [SPIRES].

  37. P. Goddard, J. Nuyts and D.I. Olive, Gauge theories and magnetic charge, Nucl. Phys. B 125 (1977) 1 [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  38. Y. Imamura and S. Yokoyama, Index for three dimensional superconformal field theories with general R-charge assignments, JHEP 04 (2011) 007 [arXiv:1101.0557] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  39. A.J. Niemi and G.W. Semenoff, Axial anomaly induced fermion fractionization and effective gauge theory actions in odd dimensional space-times, Phys. Rev. Lett. 51 (1983) 2077 [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  40. A.N. Redlich, Gauge noninvariance and parity nonconservation of three-dimensional fermions, Phys. Rev. Lett. 52 (1984) 18 [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  41. A.N. Redlich, Parity violation and gauge noninvariance of the effective gauge field action in three-dimensions, Phys. Rev. D 29 (1984) 2366 [SPIRES].

    ADS  MathSciNet  Google Scholar 

  42. 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] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  43. K.D. Kennaway, Brane tilings, Int. J. Mod. Phys. A 22 (2007) 2977 [arXiv:0706.1660] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  44. J. Davey, A. Hanany, N. Mekareeya and G. Torri, Phases of M2-brane theories, JHEP 06 (2009) 025 [arXiv:0903.3234] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  45. Y. Imamura and K. Kimura, Quiver Chern-Simons theories and crystals, JHEP 10 (2008) 114 [arXiv:0808.4155] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  46. J. de Boer, K. Hori and Y. Oz, Dynamics of \( \mathcal{N} = 2 \) supersymmetric gauge theories in three dimensions, Nucl. Phys. B 500 (1997) 163 [hep-th/9703100] [SPIRES].

    ADS  Google Scholar 

  47. O. Aharony, A. Hanany, K.A. Intriligator, N. Seiberg and M.J. Strassler, Aspects of \( \mathcal{N} = 2 \) supersymmetric gauge theories in three dimensions, Nucl. Phys. B 499 (1997) 67 [hep-th/9703110] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  48. N. Dorey and D. Tong, Mirror symmetry and toric geometry in three dimensional gauge theories, JHEP 05 (2000) 018 [hep-th/9911094] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  49. D. Tong, Dynamics of \( \mathcal{N} = 2 \) supersymmetric Chern-Simons theories, JHEP 07 (2000) 019 [hep-th/0005186] [SPIRES].

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  51. D. Marolf, Chern-Simons terms and the three notions of charge, hep-th/0006117 [SPIRES].

  52. J. Evslin, The cascade is a MMS instanton, hep-th/0405210 [SPIRES].

  53. F. Benini, F. Canoura, S. Cremonesi, C. Núñez and A.V. Ramallo, Backreacting flavors in the Klebanov-Strassler background, JHEP 09 (2007) 109 [arXiv:0706.1238] [SPIRES].

    Article  ADS  Google Scholar 

  54. F. Benini, A chiral cascade via backreacting D7-branes with flux, JHEP 10 (2008) 051 [arXiv:0710.0374] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  55. R. Argurio, F. Benini, M. Bertolini, C. Closset and S. Cremonesi, Gauge/gravity duality and the interplay of various fractional branes, Phys. Rev. D 78 (2008) 046008 [arXiv:0804.4470] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  56. F. Benini, M. Bertolini, C. Closset and S. Cremonesi, The \( \mathcal{N} = 2 \) cascade revisited and the enhancon bearings, Phys. Rev. D 79 (2009) 066012 [arXiv:0811.2207] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  57. O. Aharony, A. Hashimoto, S. Hirano and P. Ouyang, D-brane charges in gravitational duals of 2+ 1 dimensional gauge theories and duality cascades, JHEP 01 (2010) 072 [arXiv:0906.2390] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  58. A. Hashimoto, S. Hirano and P. Ouyang, Branes and fluxes in special holonomy manifolds and cascading field theories, JHEP 06 (2011) 101 [arXiv:1004.0903] [SPIRES].

    Article  ADS  Google Scholar 

  59. A. Hashimoto and P. Ouyang, Quantization of charges and fluxes in warped Stenzel geometry, JHEP 06 (2011) 124 [arXiv:1104.3517] [SPIRES].

    Article  ADS  Google Scholar 

  60. D.S. Freed and E. Witten, Anomalies in string theory with D-branes, hep-th/9907189 [SPIRES].

  61. O. Bergman and S. Hirano, Anomalous radius shift in AdS 4 /CFT 3, JHEP 07 (2009) 016 [arXiv:0902.1743] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

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

  63. S. Gukov, M. Rangamani and E. Witten, Dibaryons, strings and branes in AdS orbifold models, JHEP 12 (1998) 025 [hep-th/9811048] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  64. D.-E. Diaconescu and J. Gomis, Fractional branes and boundary states in orbifold theories, JHEP 10 (2000) 001 [hep-th/9906242] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  65. M.R. Douglas, B. Fiol and C. Romelsberger, The spectrum of BPS branes on a noncompact Calabi-Yau, JHEP 09 (2005) 057 [hep-th/0003263] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  66. M. Mariño, R. Minasian, G.W. Moore and A. Strominger, Nonlinear instantons from supersymmetric p-branes, JHEP 01 (2000) 005 [hep-th/9911206] [SPIRES].

    Article  ADS  Google Scholar 

  67. A. Klemm and E. Zaslow, Local mirror symmetry at higher genus, hep-th/9906046 [SPIRES].

  68. O. Aharony, D. Jafferis, A. Tomasiello and A. Zaddaroni, Massive type IIA string theory cannot be strongly coupled, JHEP 11 (2010) 047 [arXiv:1007.2451] [SPIRES].

    Article  ADS  Google Scholar 

  69. K. Behrndt and M. Cvetič, General \( \mathcal{N} = 1 \) supersymmetric fluxes in massive type IIA string theory, Nucl. Phys. B 708 (2005) 45 [hep-th/0407263] [SPIRES].

    Article  ADS  Google Scholar 

  70. D. Lüst and D. Tsimpis, Supersymmetric AdS 4 compactifications of IIA supergravity, JHEP 02 (2005) 027 [hep-th/0412250] [SPIRES].

    Article  Google Scholar 

  71. B.S. Acharya, F. Benini and R. Valandro, Fixing moduli in exact type IIA flux vacua, JHEP 02 (2007) 018 [hep-th/0607223] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  72. M. Petrini and A. Zaffaroni, \( \mathcal{N} = 2 \) solutions of massive type IIA and their Chern-Simons duals, JHEP 09 (2009) 107 [arXiv:0904.4915] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  73. D. Lüst and D. Tsimpis, New supersymmetric AdS 4 type-II vacua, JHEP 09 (2009) 098 [arXiv:0906.2561] [SPIRES].

    Article  Google Scholar 

  74. N. Benishti, Emerging non-anomalous baryonic symmetries in the AdS 5 /CFT 4 correspondence, JHEP 06 (2011) 075 [arXiv:1102.1979] [SPIRES].

    Article  ADS  Google Scholar 

  75. J. Gomis, F. Marchesano and D. Mateos, An open string landscape, JHEP 11 (2005) 021 [hep-th/0506179] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  76. J. Le Potier, Lectures on vector bundles, Cambridge University Press, Cambridge U.K. (1997).

    MATH  Google Scholar 

  77. S. Cheon, D. Gang, S. Kim and J. Park, Refined test of AdS 4 /CFT 3 correspondence for \( \mathcal{N} = 2 \) , 3 theories, JHEP 05 (2011) 027 [arXiv:1102.4273] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  78. E. Witten, On flux quantization in M-theory and the effective action, J. Geom. Phys. 22 (1997) 1 [hep-th/9609122] [SPIRES].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  79. E. Witten, Non-perturbative superpotentials in string theory, Nucl. Phys. B 474 (1996) 343 [hep-th/9604030] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  80. N. Benishti, D. Rodriguez-Gomez and J. Sparks, Baryonic symmetries and M5 branes in the AdS 4 /CFT 3 correspondence, JHEP 07 (2010) 024 [arXiv:1004.2045] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  81. D. Gaiotto and A. Tomasiello, The gauge dual of Romans mass, JHEP 01 (2010) 015 [arXiv:0901.0969] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  82. M. Fujita, W. Li, S. Ryu and T. Takayanagi, Fractional quantum Hall effect via holography: Chern-Simons, edge states and hierarchy, JHEP 06 (2009) 066 [arXiv:0901.0924] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  83. A. Tomasiello and A. Zaffaroni, Parameter spaces of massive IIA solutions, JHEP 04 (2011) 067 [arXiv:1010.4648] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  84. D.L. Jafferis, I.R. Klebanov, S.S. Pufu and B.R. Safdi, Towards the F-theorem: \( \mathcal{N} = 2 \) field theories on the three-sphere, JHEP 06 (2011) 102 [arXiv:1103.1181] [SPIRES].

    Article  ADS  Google Scholar 

  85. S. Cremonesi, Type IIB construction of flavoured ABJ(M) and fractional M2 branes, JHEP 01 (2011) 076 [arXiv:1007.4562] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  86. K. Hori, H. Ooguri and Y. Oz, Strong coupling dynamics of four-dimensional \( \mathcal{N} = 1 \) gauge theories from M-theory fivebrane, Adv. Theor. Math. Phys. 1 (1998) 1 [hep-th/9706082] [SPIRES].

    MathSciNet  Google Scholar 

  87. J. Bhattacharya, S. Bhattacharyya, S. Minwalla and S. Raju, Indices for superconformal field theories in 3, 5 and 6 dimensions, JHEP 02 (2008) 064 [arXiv:0801.1435] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  88. P.S. Aspinwall, D-branes on Calabi-Yau manifolds, hep-th/0403166 [SPIRES].

  89. Meijer G-function Wikipedia webpage, http://en.wikipedia.org/wiki/Meijer G-function.

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Authors and Affiliations

  1. Department of Physics, Princeton University, Jadwin Hall, Princeton, NJ, 08542, U.S.A.

    Francesco Benini

  2. Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot, 76100, Israel

    Cyril Closset

  3. Department of Particle Physics, Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Ramat-Aviv, 69978, Israel

    Stefano Cremonesi

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  1. Francesco Benini
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  2. Cyril Closset
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  3. Stefano Cremonesi
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Benini, F., Closset, C. & Cremonesi, S. Quantum moduli space of Chern-Simons quivers, wrapped D6-branes and AdS 4 /CFT 3 . J. High Energ. Phys. 2011, 5 (2011). https://doi.org/10.1007/JHEP09(2011)005

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