Skip to main content
SpringerLink
Log in

Inverse algorithm and M2-brane theories

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

Recent paper arXiv:1103.0553 studied the quiver gauge theories on coincident M2 branes on a singular toric Calabi-Yau 4-folds which are complex cone over toric Fano 3-folds. There are 18 toric Fano manifolds but only 14 toric Fano were obtained from the forward algorithm. We attempt to systematize the inverse algorithm which helps in obtaining quiver gauge theories on M 2-branes from the toric data of the Calabi-Yau 4-folds. In particular, we obtain quiver gauge theories on coincident M 2-branes corresponding to the remaining 4 toric Fano 3-folds. We observe that these quiver gauge theories cannot be given a dimer tiling presentation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

    MathSciNet  ADS  Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

  3. J. Bagger and N. Lambert, Comments on multiple M2-branes, JHEP 02 (2008) 105 [arXiv:0712.3738] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  5. A. Gustavsson, Selfdual strings and loop space Nahm equations, JHEP 04 (2008) 083 [arXiv:0802.3456] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. M. Van Raamsdonk, Comments on the Bagger-Lambert theory and multiple M2-branes, JHEP 05 (2008) 105 [arXiv:0803.3803] [INSPIRE].

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  8. I.R. Klebanov and G. Torri, M2-branes and AdS/CFT, Int. J. Mod. Phys. A 25 (2010) 332 [arXiv:0909.1580] [INSPIRE].

    ADS  Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

  10. 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].

    Article  MathSciNet  ADS  Google Scholar 

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

  12. 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].

    Article  MathSciNet  ADS  Google Scholar 

  13. A. Hanany and A. Zaffaroni, Tilings, Chern-Simons Theories and M2 Branes, JHEP 10 (2008) 111 [arXiv:0808.1244] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  14. K. Ueda and M. Yamazaki, Toric Calabi-Yau four-folds dual to Chern-Simons-matter theories, JHEP 12 (2008) 045 [arXiv:0808.3768] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  15. A. Hanany, D. Vegh and A. Zaffaroni, Brane Tilings and M2 Branes, JHEP 03 (2009) 012 [arXiv:0809.1440] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  16. S. Franco, A. Hanany, J. Park and D. Rodriguez-Gomez, Towards M2-brane theories for generic toric singularities, JHEP 12 (2008) 110 [arXiv:0809.3237] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  17. A. Hanany and Y.-H. He, M2-Branes and Quiver Chern-Simons: A Taxonomic Study, arXiv:0811.4044 [INSPIRE].

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

    Article  MathSciNet  ADS  Google Scholar 

  19. J. Davey, A. Hanany, N. Mekareeya and G. Torri, Higgsing M2-brane Theories, JHEP 11 (2009) 028 [arXiv:0908.4033] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  20. J. Davey, A. Hanany, N. Mekareeya and G. Torri, M2-Branes and Fano 3-folds, J. Phys. A A 44 (2011) 405401 [arXiv:1103.0553] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  21. P. Agarwal, P. Ramadevi and T. Sarkar, A Note on dimer models and D-brane gauge theories, JHEP 06 (2008) 054 [arXiv:0804.1902] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. S. Lee, Superconformal field theories from crystal lattices, Phys. Rev. D 75 (2007) 101901 [hep-th/0610204] [INSPIRE].

    ADS  Google Scholar 

  23. S. Lee, S. Lee and J. Park, Toric AdS4/CFT3 duals and M-theory Crystals, JHEP 05 (2007) 004 [hep-th/0702120] [INSPIRE].

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  25. D. Forcella and A. Zaffaroni, N = 1 Chern-Simons theories, orientifolds and Spin(7) cones, JHEP 05 (2010) 045 [arXiv:0911.2595] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Indian Institute of Technology Bombay, Mumbai, India

    Siddharth Dwivedi & Pichai Ramadevi

  2. Center for Quantum Spacetime, Sogang University, Seoul, South Korea

    Pichai Ramadevi

Authors
  1. Siddharth Dwivedi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pichai Ramadevi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pichai Ramadevi.

Additional information

ArXiv ePrint: 1108.2387

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dwivedi, S., Ramadevi, P. Inverse algorithm and M2-brane theories. J. High Energ. Phys. 2011, 111 (2011). https://doi.org/10.1007/JHEP11(2011)111

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP11(2011)111

Keywords

Search

Navigation