Abstract
We consider minimally supersymmetric QCD in 2+1 dimensions, with Chern-Simons and superpotential interactions. We propose an infrared SU(N) ↔ U(k) duality involving gauge-singlet fields on one of the two sides. It shares qualitative features both with 3d bosonization and with 4d Seiberg duality. We provide a few consistency checks of the proposal, mapping the structure of vacua and performing perturbative computations in the ε-expansion.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
O. Aharony, G. Gur-Ari and R. Yacoby, d = 3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories, JHEP 03 (2012) 037 [arXiv:1110.4382] [INSPIRE].
S. Giombi, S. Minwalla, S. Prakash, S.P. Trivedi, S.R. Wadia and X. Yin, Chern-Simons Theory with Vector Fermion Matter, Eur. Phys. J. C 72 (2012) 2112 [arXiv:1110.4386] [INSPIRE].
M. Barkeshli and J. McGreevy, Continuous transition between fractional quantum Hall and superfluid states, Phys. Rev. B 89 (2014) 235116 [arXiv:1201.4393] [INSPIRE].
O. Aharony, G. Gur-Ari and R. Yacoby, Correlation Functions of Large N Chern-Simons-Matter Theories and Bosonization in Three Dimensions, JHEP 12 (2012) 028 [arXiv:1207.4593] [INSPIRE].
S. Jain, S. Minwalla and S. Yokoyama, Chern Simons duality with a fundamental boson and fermion, JHEP 11 (2013) 037 [arXiv:1305.7235] [INSPIRE].
D.T. Son, Is the Composite Fermion a Dirac Particle?, Phys. Rev. X 5 (2015) 031027 [arXiv:1502.03446] [INSPIRE].
O. Aharony, Baryons, monopoles and dualities in Chern-Simons-matter theories, JHEP 02 (2016) 093 [arXiv:1512.00161] [INSPIRE].
A. Karch and D. Tong, Particle-Vortex Duality from 3d Bosonization, Phys. Rev. X 6 (2016) 031043 [arXiv:1606.01893] [INSPIRE].
J. Murugan and H. Nastase, Particle-vortex duality in topological insulators and superconductors, JHEP 05 (2017) 159 [arXiv:1606.01912] [INSPIRE].
N. Seiberg, T. Senthil, C. Wang and E. Witten, A Duality Web in 2 + 1 Dimensions and Condensed Matter Physics, Annals Phys. 374 (2016) 395 [arXiv:1606.01989] [INSPIRE].
P.-S. Hsin and N. Seiberg, Level/rank Duality and Chern-Simons-Matter Theories, JHEP 09 (2016) 095 [arXiv:1607.07457] [INSPIRE].
A. Karch, B. Robinson and D. Tong, More Abelian Dualities in 2 + 1 Dimensions, JHEP 01 (2017) 017 [arXiv:1609.04012] [INSPIRE].
M.A. Metlitski, A. Vishwanath and C. Xu, Duality and bosonization of (2 + 1)-dimensional Majorana fermions, Phys. Rev. B 95 (2017) 205137 [arXiv:1611.05049] [INSPIRE].
O. Aharony, F. Benini, P.-S. Hsin and N. Seiberg, Chern-Simons-matter dualities with SO and USp gauge groups, JHEP 02 (2017) 072 [arXiv:1611.07874] [INSPIRE].
F. Benini, P.-S. Hsin and N. Seiberg, Comments on global symmetries, anomalies and duality in (2 + 1)d, JHEP 04 (2017) 135 [arXiv:1702.07035] [INSPIRE].
Z. Komargodski and N. Seiberg, A symmetry breaking scenario for QCD 3, JHEP 01 (2018) 109 [arXiv:1706.08755] [INSPIRE].
J. Gomis, Z. Komargodski and N. Seiberg, Phases Of Adjoint QCD 3 And Dualities, SciPost Phys. 5 (2018) 007 [arXiv:1710.03258] [INSPIRE].
A. Armoni and V. Niarchos, Phases of QCD 3 from non-SUSY Seiberg Duality and Brane Dynamics, Phys. Rev. D 97 (2018) 106001 [arXiv:1711.04832] [INSPIRE].
C. Córdova, P.-S. Hsin and N. Seiberg, Global Symmetries, Counterterms and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups, SciPost Phys. 4 (2018) 021 [arXiv:1711.10008] [INSPIRE].
F. Benini, Three-dimensional dualities with bosons and fermions, JHEP 02 (2018) 068 [arXiv:1712.00020] [INSPIRE].
K. Jensen, A master bosonization duality, JHEP 01 (2018) 031 [arXiv:1712.04933] [INSPIRE].
C. Córdova, P.-S. Hsin and N. Seiberg, Time-Reversal Symmetry, Anomalies and Dualities in (2 + 1)d, SciPost Phys. 5 (2018) 006 [arXiv:1712.08639] [INSPIRE].
M.E. Peskin, Mandelstam ’t Hooft Duality in Abelian Lattice Models, Annals Phys. 113 (1978) 122 [INSPIRE].
C. Dasgupta and B.I. Halperin, Phase Transition in a Lattice Model of Superconductivity, Phys. Rev. Lett. 47 (1981) 1556 [INSPIRE].
K.A. Intriligator and N. Seiberg, Mirror symmetry in three-dimensional gauge theories, Phys. Lett. B 387 (1996) 513 [hep-th/9607207] [INSPIRE].
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] [INSPIRE].
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] [INSPIRE].
A. Giveon and D. Kutasov, Seiberg Duality in Chern-Simons Theory, Nucl. Phys. B 812 (2009) 1 [arXiv:0808.0360] [INSPIRE].
F. Benini, Y. Tachikawa and D. Xie, Mirrors of 3d Sicilian theories, JHEP 09 (2010) 063 [arXiv:1007.0992] [INSPIRE].
F. Benini, C. Closset and S. Cremonesi, Comments on 3d Seiberg-like dualities, JHEP 10 (2011) 075 [arXiv:1108.5373] [INSPIRE].
S.J. Gates, M.T. Grisaru, M. Roček and W. Siegel, Superspace Or One Thousand and One Lessons in Supersymmetry, Front. Phys. 58 (1983) 1 [hep-th/0108200] [INSPIRE].
N. Ohta and P.K. Townsend, Supersymmetry of M-branes at angles, Phys. Lett. B 418 (1998) 77 [hep-th/9710129] [INSPIRE].
T. Kitao, K. Ohta and N. Ohta, Three-dimensional gauge dynamics from brane configurations with (p, q)-five-brane, Nucl. Phys. B 539 (1999) 79 [hep-th/9808111] [INSPIRE].
M. Gremm and E. Katz, Mirror symmetry for \( \mathcal{N} \) = 1 QED in three-dimensions, JHEP 02 (2000) 008 [hep-th/9906020] [INSPIRE].
O. Bergman, A. Hanany, A. Karch and B. Kol, Branes and supersymmetry breaking in three-dimensional gauge theories, JHEP 10 (1999) 036 [hep-th/9908075] [INSPIRE].
S. Gukov and D. Tong, D-brane probes of special holonomy manifolds and dynamics of \( \mathcal{N} \) = 1 three-dimensional gauge theories, JHEP 04 (2002) 050 [hep-th/0202126] [INSPIRE].
H. Ooguri and C.-S. Park, Superconformal Chern-Simons Theories and the Squashed Seven Sphere, JHEP 11 (2008) 082 [arXiv:0808.0500] [INSPIRE].
A. Armoni, A. Giveon, D. Israel and V. Niarchos, Brane Dynamics and 3D Seiberg Duality on the Domain Walls of 4D \( \mathcal{N} \) = 1 SYM, JHEP 07 (2009) 061 [arXiv:0905.3195] [INSPIRE].
D. Forcella and A. Zaffaroni, \( \mathcal{N} \) = 1 Chern-Simons theories, orientifolds and Spin(7) cones, JHEP 05 (2010) 045 [arXiv:0911.2595] [INSPIRE].
A. Amariti and D. Forcella, Spin(7) duality for \( \mathcal{N} \) = 1 CS-matter theories, JHEP 07 (2014) 082 [arXiv:1404.4052] [INSPIRE].
S.-S. Lee, Emergence of supersymmetry at a critical point of a lattice model, Phys. Rev. B 76 (2007) 075103 [cond-mat/0611658] [INSPIRE].
T. Grover, D.N. Sheng and A. Vishwanath, Emergent Space-Time Supersymmetry at the Boundary of a Topological Phase, Science 344 (2014) 280 [arXiv:1301.7449] [INSPIRE].
S.-K. Jian, Y.-F. Jiang and H. Yao, Emergent Spacetime Supersymmetry in 3D Weyl Semimetals and 2D Dirac Semimetals, Phys. Rev. Lett. 114 (2015) 237001 [arXiv:1407.4497] [INSPIRE].
N. Zerf, C.-H. Lin and J. Maciejko, Superconducting quantum criticality of topological surface states at three loops, Phys. Rev. B 94 (2016) 205106 [arXiv:1605.09423] [INSPIRE].
L. Fei, S. Giombi, I.R. Klebanov and G. Tarnopolsky, Yukawa CFTs and Emergent Supersymmetry, PTEP 2016 (2016) 12C105 [arXiv:1607.05316] [INSPIRE].
S.-K. Jian, C.-H. Lin, J. Maciejko and H. Yao, Emergence of supersymmetric quantum electrodynamics, Phys. Rev. Lett. 118 (2017) 166802 [arXiv:1609.02146] [INSPIRE].
Z.-X. Li, A. Vaezi, C.B. Mendl and H. Yao, Observation of Emergent Spacetime Supersymmetry at Superconducting Quantum Criticality, arXiv:1711.04772 [INSPIRE].
N. Seiberg, Electric-magnetic duality in supersymmetric nonAbelian gauge theories, Nucl. Phys. B 435 (1995) 129 [hep-th/9411149] [INSPIRE].
N. Zerf, L.N. Mihaila, P. Marquard, I.F. Herbut and M.M. Scherer, Four-loop critical exponents for the Gross-Neveu-Yukawa models, Phys. Rev. D 96 (2017) 096010 [arXiv:1709.05057] [INSPIRE].
M. Baggio, N. Bobev, S.M. Chester, E. Lauria and S.S. Pufu, Decoding a Three-Dimensional Conformal Manifold, JHEP 02 (2018) 062 [arXiv:1712.02698] [INSPIRE].
D. Bashkirov, Bootstrapping the \( \mathcal{N} \) = 1 SCFT in three dimensions, arXiv:1310.8255 [INSPIRE].
N. Bobev, S. El-Showk, D. Mazac and M.F. Paulos, Bootstrapping the Three-Dimensional Supersymmetric Ising Model, Phys. Rev. Lett. 115 (2015) 051601 [arXiv:1502.04124] [INSPIRE].
N. Bobev, S. El-Showk, D. Mazac and M.F. Paulos, Bootstrapping SCFTs with Four Supercharges, JHEP 08 (2015) 142 [arXiv:1503.02081] [INSPIRE].
B.S. Acharya and C. Vafa, On domain walls of \( \mathcal{N} \) = 1 supersymmetric Yang-Mills in four-dimensions, hep-th/0103011 [INSPIRE].
D. Gaiotto, Z. Komargodski and N. Seiberg, Time-reversal breaking in QCD 4 , walls and dualities in 2 + 1 dimensions, JHEP 01 (2018) 110 [arXiv:1708.06806] [INSPIRE].
V. Bashmakov, J. Gomis, Z. Komargodski and A. Sharon, Phases of \( \mathcal{N} \) = 1 theories in 2 + 1 dimensions, JHEP 07 (2018) 123 [arXiv:1802.10130] [INSPIRE].
F. Benini, S. Benvenuti and S. Pasquetti, SUSY monopole potentials in 2 + 1 dimensions, JHEP 08 (2017) 086 [arXiv:1703.08460] [INSPIRE].
E. Witten, Supersymmetric index of three-dimensional gauge theory, hep-th/9903005 [INSPIRE].
I. Jack and H. Osborn, Analogs for the c Theorem for Four-dimensional Renormalizable Field Theories, Nucl. Phys. B 343 (1990) 647 [INSPIRE].
S.M. Chester, S. Giombi, L.V. Iliesiu, I.R. Klebanov, S.S. Pufu and R. Yacoby, Accidental Symmetries and the Conformal Bootstrap, JHEP 01 (2016) 110 [arXiv:1507.04424] [INSPIRE].
L. Iliesiu, F. Kos, D. Poland, S.S. Pufu, D. Simmons-Duffin and R. Yacoby, Bootstrapping 3D Fermions, JHEP 03 (2016) 120 [arXiv:1508.00012] [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: 1803.01784
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Benini, F., Benvenuti, S. \( \mathcal{N} \) = 1 dualities in 2+1 dimensions. J. High Energ. Phys. 2018, 197 (2018). https://doi.org/10.1007/JHEP11(2018)197
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2018)197