Advertisement

Exact relations between M2-brane theories with and without orientifolds

  • Masazumi HondaEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

We study partition functions of low-energy effective theories of M2-branes, whose type IIB brane constructions include orientifolds. We mainly focus on circular quiver superconformal Chern-Simons theory on S 3, whose gauge group is O(2N + 1) × USp(2N ) × ···×O(2N +1)×USp(2N). This theory is the natural generalization of the \( \mathcal{N} \) = 5 ABJM theory with the gauge group O(2N + 1)2k × USp(2N )k . We find that the partition function of this type of theory has a simple relation to the one of the M2-brane theory without the orientifolds, whose gauge group is U(N ) × · · · × U(N ). By using this relation, we determine an exact form of the grand partition function of the O(2N +1)2 ×USp(2N )−1 ABJM theory, where its supersymmetry is expected to be enhanced to \( \mathcal{N} \) = 6. As another interesting application, we discuss that our result gives a natural physical interpretation of a relation between the grand partition functions of the U(N + 1)4 × U(N )−4 ABJ theory and U(N )2 × U(N )−2 ABJM theory, recently conjectured by Grassi-Hatsuda-Mariño. We also argue that partition functions of  3 quiver theories have representations in terms of an ideal Fermi gas systems associated with \( \widehat{D} \)-type quiver theories and this leads an interesting relation between certain U(N ) and USp(2N ) supersymmetric gauge theories.

Keywords

AdS-CFT Correspondence Chern-Simons Theories Supersymmetric gauge theory Supersymmetry and Duality 

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]
    V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    A. Kapustin, B. Willett and I. Yaakov, Exact results for Wilson loops in superconformal Chern-Simons theories with matter, JHEP 03 (2010) 089 [arXiv:0909.4559] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    D.L. Jafferis, The exact superconformal R-symmetry extremizes Z, JHEP 05 (2012) 159 [arXiv:1012.3210] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  4. [4]
    N. Hama, K. Hosomichi and S. Lee, Notes on SUSY gauge theories on three-sphere, JHEP 03 (2011) 127 [arXiv:1012.3512] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    M. Mariño and P. Putrov, ABJM theory as a Fermi gas, J. Stat. Mech. 03 (2012) P03001 [arXiv:1110.4066] [INSPIRE].
  6. [6]
    Y. Hatsuda, M. Mariño, S. Moriyama and K. Okuyama, Non-perturbative effects and the refined topological string, JHEP 09 (2014) 168 [arXiv:1306.1734] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    S. Matsumoto and S. Moriyama, ABJ fractional brane from ABJM Wilson loop, JHEP 03 (2014) 079 [arXiv:1310.8051] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    M. Honda and K. Okuyama, Exact results on ABJ theory and the refined topological string, JHEP 08 (2014) 148 [arXiv:1405.3653] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    Y. Hatsuda, M. Honda, S. Moriyama and K. Okuyama, ABJM Wilson loops in arbitrary representations, JHEP 10 (2013) 168 [arXiv:1306.4297] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M 2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    O. Aharony, O. Bergman and D.L. Jafferis, Fractional M 2-branes, JHEP 11 (2008) 043 [arXiv:0807.4924] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    M. Mariño and P. Putrov, Exact results in ABJM theory from topological strings, JHEP 06 (2010) 011 [arXiv:0912.3074] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    N. Drukker, M. Mariño and P. Putrov, From weak to strong coupling in ABJM theory, Commun. Math. Phys. 306 (2011) 511 [arXiv:1007.3837] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    N. Drukker and D. Trancanelli, A supermatrix model for N = 6 super Chern-Simons-matter theory, JHEP 02 (2010) 058 [arXiv:0912.3006] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    A. Klemm, M. Mariño, M. Schiereck and M. Soroush, Aharony-Bergman-Jafferis-Maldacena Wilson loops in the Fermi gas approach, Z. Naturforsch. A 68 (2013) 178 [arXiv:1207.0611] [INSPIRE].ADSGoogle Scholar
  16. [16]
    A. Grassi, J. Kallen and M. Mariño, The topological open string wavefunction, Commun. Math. Phys. 338 (2015) 533 [arXiv:1304.6097] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    C.P. Herzog, I.R. Klebanov, S.S. Pufu and T. Tesileanu, Multi-matrix models and tri-Sasaki Einstein spaces, Phys. Rev. D 83 (2011) 046001 [arXiv:1011.5487] [INSPIRE].ADSGoogle Scholar
  18. [18]
    H. Fuji, S. Hirano and S. Moriyama, Summing up all genus free energy of ABJM matrix model, JHEP 08 (2011) 001 [arXiv:1106.4631] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    K. Okuyama, A note on the partition function of ABJM theory on S 3, Prog. Theor. Phys. 127 (2012) 229 [arXiv:1110.3555] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  20. [20]
    M. Hanada, M. Honda, Y. Honma, J. Nishimura, S. Shiba and Y. Yoshida, Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant, JHEP 05 (2012) 121 [arXiv:1202.5300] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    Y. Hatsuda, S. Moriyama and K. Okuyama, Exact results on the ABJM Fermi gas, JHEP 10 (2012) 020 [arXiv:1207.4283] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    P. Putrov and M. Yamazaki, Exact ABJM partition function from TBA, Mod. Phys. Lett. A 27 (2012) 1250200 [arXiv:1207.5066] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    Y. Hatsuda, S. Moriyama and K. Okuyama, Instanton effects in ABJM theory from Fermi gas approach, JHEP 01 (2013) 158 [arXiv:1211.1251] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  24. [24]
    F. Calvo and M. Mariño, Membrane instantons from a semiclassical TBA, JHEP 05 (2013) 006 [arXiv:1212.5118] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    H. Awata, S. Hirano and M. Shigemori, The partition function of ABJ theory, Prog. Theor. Exp. Phys. 2013 (2013) 053B04 [arXiv:1212.2966] [INSPIRE].
  26. [26]
    Y. Hatsuda, S. Moriyama and K. Okuyama, Instanton bound states in ABJM theory, JHEP 05 (2013) 054 [arXiv:1301.5184] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    M. Honda, Direct derivation of “mirror” ABJ partition function, JHEP 12 (2013) 046 [arXiv:1310.3126] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    M. Honda and S. Moriyama, Instanton effects in orbifold ABJM theory, JHEP 08 (2014) 091 [arXiv:1404.0676] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    S. Moriyama and T. Nosaka, Partition functions of superconformal Chern-Simons theories from Fermi gas approach, JHEP 11 (2014) 164 [arXiv:1407.4268] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    S. Moriyama and T. Nosaka, ABJM membrane instanton from a pole cancellation mechanism, Phys. Rev. D 92 (2015) 026003 [arXiv:1410.4918] [INSPIRE].ADSMathSciNetGoogle Scholar
  31. [31]
    S. Moriyama and T. Nosaka, Exact instanton expansion of superconformal Chern-Simons theories from topological strings, JHEP 05 (2015) 022 [arXiv:1412.6243] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  32. [32]
    Y. Hatsuda, M. Honda and K. Okuyama, Large-N non-perturbative effects in N = 4 superconformal Chern-Simons theories, JHEP 09 (2015) 046 [arXiv:1505.07120] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  33. [33]
    M. Mariño and P. Putrov, Interacting fermions and N = 2 Chern-Simons-matter theories, JHEP 11 (2013) 199 [arXiv:1206.6346] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    M. Mezei and S.S. Pufu, Three-sphere free energy for classical gauge groups, JHEP 02 (2014) 037 [arXiv:1312.0920] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    B. Assel, N. Drukker and J. Felix, Partition functions of 3d \( \widehat{D} \) -quivers and their mirror duals from 1d free fermions, JHEP 08 (2015) 071 [arXiv:1504.07636] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  36. [36]
    S. Moriyama and T. Nosaka, Superconformal Chern-Simons partition functions of affine D-type quiver from Fermi gas, JHEP 09 (2015) 054 [arXiv:1504.07710] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  37. [37]
    S. Bhattacharyya, A. Grassi, M. Mariño and A. Sen, A one-loop test of quantum supergravity, Class. Quant. Grav. 31 (2014) 015012 [arXiv:1210.6057] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  38. [38]
    A. Dabholkar, N. Drukker and J. Gomes, Localization in supergravity and quantum AdS 4 /CFT 3 holography, JHEP 10 (2014) 090 [arXiv:1406.0505] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  39. [39]
    Y. Imamura and K. Kimura, On the moduli space of elliptic Maxwell-Chern-Simons theories, Prog. Theor. Phys. 120 (2008) 509 [arXiv:0806.3727] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  40. [40]
    D. Gaiotto and E. Witten, Janus configurations, Chern-Simons couplings, and the θ-angle in N =4 super Yang-Mills theory, JHEP 06(2010) 097[arXiv:0804.2907] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  41. [41]
    K. Hosomichi, K.-M. Lee, S. Lee, S. Lee and J. Park, N = 4 superconformal Chern-Simons theories with hyper and twisted hyper multiplets, JHEP 07 (2008) 091 [arXiv:0805.3662] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  42. [42]
    A. Grassi and M. Mariño, M-theoretic matrix models, JHEP 02 (2015) 115 [arXiv:1403.4276] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  43. [43]
    Y. Hatsuda and K. Okuyama, Probing non-perturbative effects in M-theory, JHEP 10 (2014) 158 [arXiv:1407.3786] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  44. [44]
    K. Okuyama, Probing non-perturbative effects in M-theory on orientifolds, JHEP 01 (2016) 054 [arXiv:1511.02635] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  45. [45]
    D.R. Gulotta, J.P. Ang and C.P. Herzog, Matrix models for supersymmetric Chern-Simons theories with an ADE classification, JHEP 01 (2012) 132 [arXiv:1111.1744] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  46. [46]
    D.R. Gulotta, C.P. Herzog and T. Nishioka, The ABCDEF’s of matrix models for supersymmetric Chern-Simons theories, JHEP 04 (2012) 138 [arXiv:1201.6360] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  47. [47]
    P.M. Crichigno, C.P. Herzog and D. Jain, Free energy of D n quiver Chern-Simons theories, JHEP 03 (2013) 039 [arXiv:1211.1388] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  48. [48]
    S. Moriyama and T. Suyama, Instanton effects in orientifold ABJM theory, JHEP 03 (2016) 034 [arXiv:1511.01660] [INSPIRE].ADSCrossRefGoogle Scholar
  49. [49]
    K. Hosomichi, K.-M. Lee, S. Lee, S. Lee and J. Park, N = 5, 6 superconformal Chern-Simons theories and M 2-branes on orbifolds, JHEP 09 (2008) 002 [arXiv:0806.4977] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  50. [50]
    A. Grassi, Y. Hatsuda and M. Mariño, Quantization conditions and functional equations in ABJ(M) theories, J. Phys. A 49 (2016) 115401 [arXiv:1410.7658] [INSPIRE].ADSMathSciNetGoogle Scholar
  51. [51]
    S. Codesido, A. Grassi and M. Mariño, Exact results in N = 8 Chern-Simons-matter theories and quantum geometry, JHEP 07 (2015) 011 [arXiv:1409.1799] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  52. [52]
    S. Cheon, D. Gang, C. Hwang, S. Nagaoka and J. Park, Duality between N = 5 and N = 6 Chern-Simons matter theory, JHEP 11 (2012) 009 [arXiv:1208.6085] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  53. [53]
    K.A. Intriligator and N. Seiberg, Mirror symmetry in three-dimensional gauge theories, Phys. Lett. B 387 (1996) 513 [hep-th/9607207] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  54. [54]
    A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152 [hep-th/9611230] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  55. [55]
    J. de Boer, K. Hori, H. Ooguri and Y. Oz, Mirror symmetry in three-dimensional gauge theories, quivers and D-branes, Nucl. Phys. B 493 (1997) 101 [hep-th/9611063] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  56. [56]
    B. Assel, Hanany-Witten effect and SL(2, Z) dualities in matrix models, JHEP 10 (2014) 117 [arXiv:1406.5194] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  57. [57]
    N. Drukker and J. Felix, 3d mirror symmetry as a canonical transformation, JHEP 05 (2015) 004 [arXiv:1501.02268] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  58. [58]
    S. Moriyama and T. Suyama, Orthosymplectic Chern-Simons matrix model and chirality projection, JHEP 04 (2016) 132 [arXiv:1601.03846] [INSPIRE].ADSCrossRefGoogle Scholar
  59. [59]
    A. Kapustin, B. Willett and I. Yaakov, Nonperturbative tests of three-dimensional dualities, JHEP 10 (2010) 013 [arXiv:1003.5694] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Department of Particle Physics and AstrophysicsWeizmann Institute of ScienceRehovotIsrael

Personalised recommendations