Abstract
We investigate features of duality in three dimensional \( \mathcal{N} = 2 \) Chern-Simons matter theories conjectured to describe M2 branes at toric Calabi Yau four-fold singularities. For 3D theories with non-chiral 4D parents we propone a Seiberg-like duality which turns out to be a toric duality. For theories with chiral 4D parents we discuss the conditions under which that Seiberg-like duality leads to toric duality. We comment on such duality in 3D theories without 4D parents.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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] [SPIRES].
B. Feng, A. Hanany and Y.-H. He, Phase structure of D-brane gauge theories and toric duality, JHEP 08 (2001) 040 [hep-th/0104259] [SPIRES].
B. Feng, S. Franco, A. Hanany and Y.-H. He, Symmetries of toric duality, JHEP 12 (2002) 076 [hep-th/0205144] [SPIRES].
C.E. Beasley and M.R. Plesser, Toric duality is Seiberg duality, JHEP 12 (2001) 001 [hep-th/0109053] [SPIRES].
B. Feng, A. Hanany, Y.-H. He and A.M. Uranga, Toric duality as Seiberg duality and brane diamonds, JHEP 12 (2001) 035 [hep-th/0109063] [SPIRES].
J.H. Schwarz, Superconformal Chern-Simons theories, JHEP 11 (2004) 078 [hep-th/0411077] [SPIRES].
J. Bagger and N. Lambert, Modeling multiple M2’s, Phys. Rev. D 75 (2007) 045020 [hep-th/0611108] [SPIRES].
J. Bagger and N. Lambert, Gauge symmetry and supersymmetry of multiple M2-branes, Phys. Rev. D 77 (2008) 065008 [arXiv:0711.0955] [SPIRES].
J. Bagger and N. Lambert, Comments on multiple M2-branes, JHEP 02 (2008) 105 [arXiv:0712.3738] [SPIRES].
A. Gustavsson, Algebraic structures on parallel M2-branes, Nucl. Phys. B 811 (2009) 66 [arXiv:0709.1260] [SPIRES].
A. Gustavsson, Selfdual strings and loop space Nahm equations, JHEP 04 (2008) 083 [arXiv:0802.3456] [SPIRES].
M. Van Raamsdonk, Comments on the Bagger-Lambert theory and multiple M2-branes, JHEP 05 (2008) 105 [arXiv:0803.3803] [SPIRES].
S. Mukhi and C. Papageorgakis, M2 to D2, JHEP 05 (2008) 085 [arXiv:0803.3218] [SPIRES].
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].
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].
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].
K. Hosomichi, K.-M. Lee, S. Lee, S. Lee and J. Park, \( \mathcal{N} = 4 \) superconformal Chern-Simons theories with hyper and twisted hyper multiplets, JHEP 07 (2008) 091 [arXiv:0805.3662] [SPIRES].
K. Hosomichi, K.-M. Lee, S. Lee, S. Lee and J. Park, \( \mathcal{N} = 5,6 \) superconformal Chern-Simons theories and M2-branes on orbifolds, JHEP 09 (2008) 002 [arXiv:0806.4977] [SPIRES].
M. Schnabl and Y. Tachikawa, Classification of \( \mathcal{N} = 6 \) superconformal theories of ABJM type, arXiv:0807.1102 [SPIRES].
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].
A. Hanany and A. Zaffaroni, Tilings, Chern-Simons theories and M2 branes, JHEP 10 (2008) 111 [arXiv:0808.1244] [SPIRES].
A. Hanany, D. Vegh and A. Zaffaroni, Brane tilings and M2 branes, JHEP 03 (2009) 012 [arXiv:0809.1440] [SPIRES].
D.L. Jafferis and A. Tomasiello, A simple class of \( \mathcal{N} = 3 \) gauge/gravity duals, JHEP 10 (2008) 101 [arXiv:0808.0864] [SPIRES].
D. Gaiotto and A. Tomasiello, The gauge dual of Romans mass, JHEP 01 (2010) 015 [arXiv:0901.0969] [SPIRES].
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].
Y. Imamura and K. Kimura, \( \mathcal{N} = 4 \) Chern-Simons theories with auxiliary vector multiplets, JHEP 10 (2008) 040 [arXiv:0807.2144] [SPIRES].
Y. Imamura and S. Yokoyama, \( \mathcal{N} = 4 \) Chern-Simons theories and wrapped M5-branes in their gravity duals, Prog. Theor. Phys. 121 (2009) 915 [arXiv:0812.1331] [SPIRES].
A. Hanany and Y.-H. He, M2-branes and quiver Chern-Simons: a taxonomic study, arXiv:0811.4044 [SPIRES].
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] [SPIRES].
K. Ueda and M. Yamazaki, Toric Calabi-Yau four-folds dual to Chern-Simons-matter theories, JHEP 12 (2008) 045 [arXiv:0808.3768] [SPIRES].
Y. Imamura and K. Kimura, Quiver Chern-Simons theories and crystals, JHEP 10 (2008) 114 [arXiv:0808.4155] [SPIRES].
A. Kapustin and M.J. Strassler, On mirror symmetry in three dimensional Abelian gauge theories, JHEP 04 (1999) 021 [hep-th/9902033] [SPIRES].
K.A. Intriligator and N. Seiberg, Mirror symmetry in three dimensional gauge theories, Phys. Lett. B 387 (1996) 513 [hep-th/9607207] [SPIRES].
O. Aharony, O. Bergman and D.L. Jafferis, Fractional M2-branes, JHEP 11 (2008) 043 [arXiv:0807.4924] [SPIRES].
A. Giveon and D. Kutasov, Seiberg duality in Chern-Simons theory, Nucl. Phys. B 812 (2009) 1 [arXiv:0808.0360] [SPIRES].
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].
A. Karch, Seiberg duality in three dimensions, Phys. Lett. B 405 (1997) 79 [hep-th/9703172] [SPIRES].
O. Aharony, IR duality in D = 3 \( \mathcal{N} = 2 \) supersymmetric USp(2N c ) and U(N c ) gauge theories, Phys. Lett. B 404 (1997) 71 [hep-th/9703215] [SPIRES].
D. Forcella, A. Hanany, Y.-H. He and A. Zaffaroni, The master space of \( \mathcal{N} = 1 \) gauge theories, JHEP 08 (2008) 012 [arXiv:0801.1585] [SPIRES].
D. Forcella, A. Hanany, Y.-H. He and A. Zaffaroni, Mastering the master space, Lett. Math. Phys. 85 (2008) 163 [arXiv:0801.3477] [SPIRES].
D. Forcella, A. Hanany and A. Zaffaroni, Master space, Hilbert series and Seiberg duality, JHEP 07 (2009) 018 [arXiv:0810.4519] [SPIRES].
S. Benvenuti and M. Kruczenski, From Sasaki-Einstein spaces to quivers via BPS geodesics: L p,q|r, JHEP 04 (2006) 033 [hep-th/0505206] [SPIRES].
A. Butti, D. Forcella and A. Zaffaroni, The dual superconformal theory for L p,q|r manifolds, JHEP 09 (2005) 018 [hep-th/0505220] [SPIRES].
S. Franco et al., Gauge theories from toric geometry and brane tilings, JHEP 01 (2006) 128 [hep-th/0505211] [SPIRES].
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].
T. Kitao, K. Ohta and N. Ohta, Three-dimensional gauge dynamics from brane configurations with (p,q)-fivebrane, Nucl. Phys. B 539 (1999) 79 [hep-th/9808111] [SPIRES].
O. Bergman, A. Hanany, A. Karch and B. Kol, Branes and supersymmetry breaking in 3D gauge theories, JHEP 10 (1999) 036 [hep-th/9908075] [SPIRES].
A.M. Uranga, Brane configurations for branes at conifolds, JHEP 01 (1999) 022 [hep-th/9811004] [SPIRES].
S. Elitzur, A. Giveon and D. Kutasov, Branes and \( \mathcal{N} = 1 \) duality in string theory, Phys. Lett. B 400 (1997) 269 [hep-th/9702014] [SPIRES].
V. Niarchos, Seiberg duality in Chern-Simons theories with fundamental and adjoint matter, JHEP 11 (2008) 001 [arXiv:0808.2771] [SPIRES].
E. Witten, Supersymmetric index of three-dimensional gauge theory, hep-th/9903005 [SPIRES].
K. Ohta, Supersymmetric index and s-rule for type IIB branes, JHEP 10 (1999) 006 [hep-th/9908120] [SPIRES].
A. Hanany and K.D. Kennaway, Dimer models and toric diagrams, hep-th/0503149 [SPIRES].
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] [SPIRES].
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].
L. Álvarez-Gaumé and E. Witten, Gravitational anomalies, Nucl. Phys. B 234 (1984) 269 [SPIRES].
A.N. Redlich, Parity violation and gauge noninvariance of the effective gauge field action in three-dimensions, Phys. Rev. D 29 (1984) 2366 [SPIRES].
S. Kim, S. Lee, S. Lee and J. Park, Abelian gauge theory on M2-brane and toric duality, Nucl. Phys. B 797 (2008) 340 [arXiv:0705.3540] [SPIRES].
S. Franco, I.R. Klebanov and D. Rodriguez-Gomez, M2-branes on orbifolds of the cone over Q 1,1,1, JHEP 08 (2009) 033 [arXiv:0903.3231] [SPIRES].
J. Davey, A. Hanany, N. Mekareeya and G. Torri, Phases of M2-brane theories, JHEP 06 (2009) 025 [arXiv:0903.3234] [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Amariti, A., Forcella, D., Girardello, L. et al. 3D Seiberg-like dualities and M2 branes. J. High Energ. Phys. 2010, 25 (2010). https://doi.org/10.1007/JHEP05(2010)025
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2010)025