Abstract
We construct a three-dimensional deconfinement method which enables us to find new three-dimensional dualities and we apply various techniques developed in the fourdimensional supersymmetric gauge theories, such as product gauge groups and SeibergWitten curves, to the three-dimensional \( \mathcal{N}=2 \) supersymmetric gauge theories. The dual descriptions of the three-dimensional \( \mathcal{N}=2 \) supersymmetric gauge theories which involve two-index matters, for example, adjoint, symmetric, and anti-symmetric matters without a superpotential can be obtained. These matters are described in terms of the s-confining phases of the supersymmetric gauge theories.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N. Seiberg, Electric-magnetic duality in supersymmetric nonAbelian gauge theories, Nucl. Phys. B 435 (1995) 129 [hep-th/9411149] [INSPIRE].
K.A. Intriligator, R.G. Leigh and M.J. Strassler, New examples of duality in chiral and nonchiral supersymmetric gauge theories, Nucl. Phys. B 456 (1995) 567 [hep-th/9506148] [INSPIRE].
M. Berkooz, The Dual of supersymmetric SU(2K) with an antisymmetric tensor and composite dualities, Nucl. Phys. B 452 (1995) 513 [hep-th/9505067] [INSPIRE].
P. Pouliot, Duality in SUSY SU(N) with an antisymmetric tensor, Phys. Lett. B 367 (1996) 151 [hep-th/9510148] [INSPIRE].
M.A. Luty, M. Schmaltz and J. Terning, A sequence of duals for Sp(2N) supersymmetric gauge theories with adjoint matter, Phys. Rev. D 54 (1996) 7815 [hep-th/9603034] [INSPIRE].
I. Affleck, J.A. Harvey and E. Witten, Instantons and (Super)Symmetry Breaking in (2+1)-Dimensions, Nucl. Phys. B 206 (1982) 413 [INSPIRE].
O. Aharony, A. Hanany, K.A. Intriligator, N. Seiberg and M.J. Strassler, Aspects of N = 2 supersymmetric gauge theories in three-dimensions, Nucl. Phys. B 499 (1997) 67 [hep-th/9703110] [INSPIRE].
J. de Boer, K. Hori and Y. Oz, Dynamics of N = 2 supersymmetric gauge theories in three-dimensions, Nucl. Phys. B 500 (1997) 163 [hep-th/9703100] [INSPIRE].
A. Giveon and D. Kutasov, Seiberg Duality in Chern-Simons Theory, Nucl. Phys. B 812 (2009) 1 [arXiv:0808.0360] [INSPIRE].
O. Aharony, IR duality in D = 3 N = 2 supersymmetric USp(2N c ) and U(N c ) gauge theories, Phys. Lett. B 404 (1997) 71 [hep-th/9703215] [INSPIRE].
V. Niarchos, Seiberg Duality in Chern-Simons Theories with Fundamental and Adjoint Matter, JHEP 11 (2008) 001 [arXiv:0808.2771] [INSPIRE].
V. Niarchos, R-charges, Chiral Rings and RG Flows in Supersymmetric Chern-Simons-Matter Theories, JHEP 05 (2009) 054 [arXiv:0903.0435] [INSPIRE].
H. Kim and J. Park, Aharony Dualities for 3d Theories with Adjoint Matter, JHEP 06 (2013) 106 [arXiv:1302.3645] [INSPIRE].
J. Park and K.-J. Park, Seiberg-like Dualities for 3d N = 2 Theories with SU(N) gauge group, JHEP 10 (2013) 198 [arXiv:1305.6280] [INSPIRE].
K. Intriligator and N. Seiberg, Aspects of 3d N = 2 Chern-Simons-Matter Theories, JHEP 07 (2013) 079 [arXiv:1305.1633] [INSPIRE].
K. Intriligator, Matching 3d N = 2 vortices and monopole operators, JHEP 10 (2014) 52 [arXiv:1406.2638] [INSPIRE].
O. Aharony, S.S. Razamat, N. Seiberg and B. Willett, 3d dualities from 4d dualities, JHEP 07 (2013) 149 [arXiv:1305.3924] [INSPIRE].
O. Aharony, S.S. Razamat, N. Seiberg and B. Willett, 3d dualities from 4d dualities for orthogonal groups, JHEP 08 (2013) 099 [arXiv:1307.0511] [INSPIRE].
A. Amariti, D. Forcella, C. Klare, D. Orlando and S. Reffert, The braneology of 3D dualities, J. Phys. A 48 (2015) 265401 [arXiv:1501.06571] [INSPIRE].
A. Amariti, D. Forcella, C. Klare, D. Orlando and S. Reffert, 4D/3D reduction of dualities: mirrors on the circle, JHEP 10 (2015) 048 [arXiv:1504.02783] [INSPIRE].
K.A. Intriligator and N. Seiberg, Phases of N = 1 supersymmetric gauge theories in four-dimensions, Nucl. Phys. B 431 (1994) 551 [hep-th/9408155] [INSPIRE].
K.A. Intriligator, R.G. Leigh and N. Seiberg, Exact superpotentials in four-dimensions, Phys. Rev. D 50 (1994) 1092 [hep-th/9403198] [INSPIRE].
C. Csáki, J. Erlich, D.Z. Freedman and W. Skiba, N=1 supersymmetric product group theories in the Coulomb phase, Phys. Rev. D 56 (1997) 5209 [hep-th/9704067] [INSPIRE].
N. Seiberg and E. Witten, Gauge dynamics and compactification to three-dimensions, hep-th/9607163 [INSPIRE].
C. Csáki, M. Martone, Y. Shirman, P. Tanedo and J. Terning, Dynamics of 3D SUSY Gauge Theories with Antisymmetric Matter, JHEP 08 (2014) 141 [arXiv:1406.6684] [INSPIRE].
A. Karch, Seiberg duality in three-dimensions, Phys. Lett. B 405 (1997) 79 [hep-th/9703172] [INSPIRE].
C. Callias, Index Theorems on Open Spaces, Commun. Math. Phys. 62 (1978) 213 [INSPIRE].
E.J. Weinberg, Fundamental Monopoles and Multi-Monopole Solutions for Arbitrary Simple Gauge Groups, Nucl. Phys. B 167 (1980) 500 [INSPIRE].
E.J. Weinberg, Fundamental Monopoles in Theories With Arbitrary Symmetry Breaking, Nucl. Phys. B 203 (1982) 445 [INSPIRE].
T. Hirayama and K. Yoshioka, Duality between simple group gauge theories and some applications, Phys. Rev. D 59 (1999) 105005 [hep-th/9811119] [INSPIRE].
A. Amariti, C. Csáki, M. Martone and N. R.-L. Lorier, From 4D to 3D chiral theories: Dressing the monopoles, Phys. Rev. D 93 (2016) 105027 [arXiv:1506.01017] [INSPIRE].
H. Murayama, Studying noncalculable models of dynamical supersymmetry breaking, Phys. Lett. B 355 (1995) 187 [hep-th/9505082] [INSPIRE].
E. Poppitz and S.P. Trivedi, Some examples of chiral moduli spaces and dynamical supersymmetry breaking, Phys. Lett. B 365 (1996) 125 [hep-th/9507169] [INSPIRE].
C. Csáki, M. Schmaltz and W. Skiba, A systematic approach to confinement in N = 1 supersymmetric gauge theories, Phys. Rev. Lett. 78 (1997) 799 [hep-th/9610139] [INSPIRE].
C. Csáki, M. Schmaltz and W. Skiba, Confinement in N = 1 SUSY gauge theories and model building tools, Phys. Rev. D 55 (1997) 7840 [hep-th/9612207] [INSPIRE].
C. Csáki, The confining N = 1 supersymmetric gauge theories: A review, hep-th/9807222 [INSPIRE].
C. Csáki and W. Skiba, Classification of the N = 1 Seiberg-Witten theories, Phys. Rev. D 58 (1998) 045008 [hep-th/9801173] [INSPIRE].
M. Gremm, The Coulomb branch of N = 1 supersymmetric SU(N c ) × SU(N c ) gauge theories, Phys. Rev. D 57 (1998) 2537 [hep-th/9707071] [INSPIRE].
O. Aharony and I. Shamir, On O(N c ) D = 3 N = 2 supersymmetric QCD Theories, JHEP 12 (2011) 043 [arXiv:1109.5081] [INSPIRE].
J. Lee and M. Yamazaki, Gauging and decoupling in 3d \( \mathcal{N}=2 \) dualities, JHEP 06 (2016) 077 [arXiv:1603.02283] [INSPIRE].
K.A. Intriligator and N. Seiberg, Duality, monopoles, dyons, confinement and oblique confinement in supersymmetric SO(N c ) gauge theories, Nucl. Phys. B 444 (1995) 125 [hep-th/9503179] [INSPIRE].
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].
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].
A. Kapustin, B. Willett and I. Yaakov, Nonperturbative Tests of Three-Dimensional Dualities, JHEP 10 (2010) 013 [arXiv:1003.5694] [INSPIRE].
N. Hama, K. Hosomichi and S. Lee, Notes on SUSY Gauge Theories on Three-Sphere, JHEP 03 (2011) 127 [arXiv:1012.3512] [INSPIRE].
Y. Imamura and S. Yokoyama, Index for three dimensional superconformal field theories with general R-charge assignments, JHEP 04 (2011) 007 [arXiv:1101.0557] [INSPIRE].
F. Benini, C. Closset and S. Cremonesi, Comments on 3d Seiberg-like dualities, JHEP 10 (2011) 075 [arXiv:1108.5373] [INSPIRE].
O. Aharony and D. Fleischer, IR Dualities in General 3d Supersymmetric SU(N ) QCD Theories, JHEP 02 (2015) 162 [arXiv:1411.5475] [INSPIRE].
K.-M. Lee and P. Yi, Monopoles and instantons on partially compactified D-branes, Phys. Rev. D 56 (1997) 3711 [hep-th/9702107] [INSPIRE].
N. Seiberg and E. Witten, Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD, Nucl. Phys. B 431 (1994) 484 [hep-th/9408099] [INSPIRE].
R. Boels, J. de Boer, R. Duivenvoorden and J. Wijnhout, Nonperturbative superpotentials and compactification to three-dimensions, JHEP 03 (2004) 009 [hep-th/0304061] [INSPIRE].
R. Boels and J. de Boer, Classical spin chains and exact three-dimensional superpotentials, Nucl. Phys. B 715 (2005) 234 [hep-th/0411110] [INSPIRE].
R. Boels, J. de Boer, R. Duivenvoorden and J. Wijnhout, Factorization of Seiberg-Witten curves and compactification to three-dimensions, JHEP 03 (2004) 010 [hep-th/0305189] [INSPIRE].
N. Dorey, An elliptic superpotential for softly broken N = 4 supersymmetric Yang-Mills theory, JHEP 07 (1999) 021 [hep-th/9906011] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1603.08550
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Nii, K. 3d deconfinement, product gauge group, Seiberg-Witten and new 3d dualities. J. High Energ. Phys. 2016, 123 (2016). https://doi.org/10.1007/JHEP08(2016)123
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2016)123