You have just completed your registration at OpenAire.
Before you can login to the site, you will need to activate your account.
An e-mail will be sent to you with the proper instructions.
Important!
Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version
of the site upon release.
arxiv:Mathematics::Symplectic Geometry, High Energy Physics::Theory, Mathematics::Algebraic Geometry
We initiate a systematic investigation of the space of 2+1 dimensional quiver gauge theories, emphasising a succinct "forward algorithm". Few "order parametres" are introduced such as the number of terms in the superpotential and the number of gauge groups. Starting with two terms in the superpotential, we find a generating function, with interesting geometric interpretation, which counts the number of inequivalent theories for a given number of gauge groups and fields. We demonstratively list these theories for some low numbers thereof. Furthermore, we show how these theories arise from M2-branes probing toric Calabi-Yau 4-folds by explicitly obtaining the toric data of the vacuum moduli space. By observing equivalences of the vacua between markedly different theories, we see a new emergence of "toric duality".
[1] J. Bagger and N. Lambert, “Modeling multiple M2's,” Phys. Rev. D 75, 045020 (2007) [arXiv:hep-th/0611108]. “Gauge Symmetry and Supersymmetry of Multiple M2- Branes,” Phys. Rev. D 77, 065008 (2008) [arXiv:0711.0955 [hep-th]]. “Comments On Multiple M2-branes,” JHEP 0802, 105 (2008) [arXiv:0712.3738 [hep-th]].
[2] A. Gustavsson, “Algebraic structures on parallel M2-branes,” arXiv:0709.1260 [hepth]. “Selfdual strings and loop space Nahm equations,” JHEP 0804, 083 (2008) [arXiv:0802.3456 [hep-th]].
[3] M. Van Raamsdonk, “Comments on the Bagger-Lambert theory and multiple M2- branes,” JHEP 0805, 105 (2008) [arXiv:0803.3803 [hep-th]].
[4] O. Aharony, O. Bergman, D. L. Jafferis and J. Maldacena, “N=6 superconformal ChernSimons-matter theories, M2-branes and their gravity duals,” arXiv:0806.1218 [hep-th].
[11] B. Feng, Y. H. He, K. D. Kennaway and C. Vafa, “Dimer models from mirror symmetry and quivering amoebae,” Adv. Theor. Math. Phys. 12, 3 (2008) [arXiv:hep-th/0511287].
[12] N. Lambert and D. Tong, “Membranes on an Orbifold,” Phys. Rev. Lett. 101, 041602 (2008) [arXiv:0804.1114 [hep-th]].
[13] A. Hanany and A. Zaffaroni, “Tilings, Chern-Simons Theories and M2 Branes,” arXiv:0808.1244 [hep-th].
[14] A. Hanany, D. Vegh, A. Zaffaroni, “Brane Tilings and M2 Branes,” arXiv:0809.1440.
[15] S. Franco, A. Hanany, J. Park and D. Rodriguez-Gomez, “Towards M2-brane Theories for Generic Toric Singularities,” arXiv:0809.3237 [hep-th].
[16] M. Benna, I. Klebanov, T. Klose, M. Smedback, “Superconformal Chern-Simons Theories and AdS4/CFT3 Correspondence,” JHEP 0809, 072 (2008) [arXiv:0806.1519].
[17] K. Hosomichi, K. M. Lee, S. Lee, S. Lee and J. Park, “N=5,6 Superconformal Chern-Simons Theories and M2-branes on Orbifolds,” JHEP 0809, 002 (2008) [arXiv:0806.4977 [hep-th]].
[18] K. Ueda and M. Yamazaki, “Toric Calabi-Yau four-folds dual to Chern-Simons-matter theories,” arXiv:0808.3768 [hep-th].
[19] Y. Imamura and K. Kimura, “Quiver Chern-Simons theories and crystals,” arXiv:0808.4155 [hep-th].
[20] S. Kim, S. Lee, S. Lee and J. Park, “Abelian Gauge Theory on M2-brane and Toric Duality,” Nucl. Phys. B 797, 340 (2008) [arXiv:0705.3540 [hep-th]].
[21] S. Lee, S. Lee and J. Park, “Toric AdS(4)/CFT(3) duals and M-theory crystals,” JHEP 0705, 004 (2007) [arXiv:hep-th/0702120].
[26] M. R. Douglas, B. R. Greene and D. R. Morrison, “Orbifold resolution by D-branes,” Nucl. Phys. B 506, 84 (1997) [arXiv:hep-th/9704151].
[30] T. Sarkar, “D-brane gauge theories from toric singularities of the form C(3)/Gamma and C(4)/Gamma,” Nucl. Phys. B 595, 201 (2001) [arXiv:hep-th/0005166].
[31] P. Agarwal, P. Ramadevi and T. Sarkar, “A Note on Dimer Models and D-brane Gauge Theories,” arXiv:0804.1902 [hep-th].
[32] T. Muto, “D-geometric structure of orbifolds,” arXiv:hep-th/0206012.
[33] L. B. Anderson, Y. H. He and A. Lukas, “Monad Bundles in Heterotic String Compactifications,” JHEP 0807, 104 (2008) [arXiv:0805.2875 [hep-th]].