Abstract
In this paper we study dualities for \( \mathcal{N} \) = 2 gauge theories in three dimensions with matter in the fundamental and adjoint representation. The duality we propose, analogous to mirror symmetry, is obtained starting from \( \mathcal{N} \) = 4 mirror theories and turning on a certain superpotential deformation involving monopole operators. We study the role of emergent symmetries in the dual theory, focusing on the case of models with gauge symmetry U(2) or SU(2). We find that SU(2) adjoint SQCD with one flavor and zero superpotential is dual to SQED with two flavors and three singlets. As a byproduct, we recover several dualities for theories with \( \mathcal{N} \) = 2 and \( \mathcal{N} \) = 4 supersymmetry, including the duality appetizer of Jafferis and Yin.
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References
K.A. Intriligator and N. Seiberg, Mirror symmetry in three-dimensional gauge theories, Phys. Lett. B 387 (1996) 513 [hep-th/9607207] [INSPIRE].
A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152 [hep-th/9611230] [INSPIRE].
J. de Boer, K. Hori, H. Ooguri and Y. Oz, Mirror symmetry in three-dimensional gauge theories, quivers and D-branes, Nucl. Phys. B 493 (1997) 101 [hep-th/9611063] [INSPIRE].
M. Porrati and A. Zaffaroni, M theory origin of mirror symmetry in three-dimensional gauge theories, Nucl. Phys. B 490 (1997) 107 [hep-th/9611201] [INSPIRE].
J. de Boer, K. Hori, H. Ooguri, Y. Oz and Z. Yin, Mirror symmetry in three-dimensional theories, SL(2, ℤ) and D-brane moduli spaces, Nucl. Phys. B 493 (1997) 148 [hep-th/9612131] [INSPIRE].
J. de Boer, K. Hori, Y. Oz and Z. Yin, Branes and mirror symmetry in N = 2 supersymmetric gauge theories in three-dimensions, Nucl. Phys. B 502 (1997) 107 [hep-th/9702154] [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].
B. Assel, Hanany-Witten effect and SL(2, ℤ) dualities in matrix models, JHEP 10 (2014) 117 [arXiv:1406.5194] [INSPIRE].
S. Benvenuti and S. Pasquetti, 3d \( \mathcal{N} \) = 2 mirror symmetry, pq-webs and monopole superpotentials, JHEP 08 (2016) 136 [arXiv:1605.02675] [INSPIRE].
S. Giacomelli and N. Mekareeya, Mirror theories of 3d \( \mathcal{N} \) = 2 SQCD, JHEP 03 (2018) 126 [arXiv:1711.11525] [INSPIRE].
M. Fazzi, A. Lanir, S.S. Razamat and O. Sela, Chiral 3d SU(3) SQCD and \( \mathcal{N} \) = 2 mirror duality, JHEP 11 (2018) 025 [arXiv:1808.04173] [INSPIRE].
S.M. Chester, L.V. Iliesiu, M. Mezei and S.S. Pufu, Monopole Operators in U(1) Chern-Simons-Matter Theories, JHEP 05 (2018) 157 [arXiv:1710.00654] [INSPIRE].
B. Assel, Note on Monopole Operators in Chern-Simons-Matter Theories, arXiv:1811.11111 [INSPIRE].
O. Aharony, S.S. Razamat, N. Seiberg and B. Willett, 3d dualities from 4d dualities, JHEP 07 (2013) 149 [arXiv:1305.3924] [INSPIRE].
A. Collinucci, S. Giacomelli, R. Savelli and R. Valandro, T-branes through 3d mirror symmetry, JHEP 07 (2016) 093 [arXiv:1603.00062] [INSPIRE].
F. Benini, S. Benvenuti and S. Pasquetti, SUSY monopole potentials in 2+1 dimensions, JHEP 08 (2017) 086 [arXiv:1703.08460] [INSPIRE].
A. Collinucci, S. Giacomelli and R. Valandro, T-branes, monopoles and S-duality, JHEP 10 (2017) 113 [arXiv:1703.09238] [INSPIRE].
A. Amariti, D. Orlando and S. Reffert, Monopole Quivers and new 3D N = 2 dualities, Nucl. Phys. B 924 (2017) 153 [arXiv:1705.09297] [INSPIRE].
A. Amariti, I. Garozzo and N. Mekareeya, New 3d \( \mathcal{N} \) = 2 dualities from quadratic monopoles, JHEP 11 (2018) 135 [arXiv:1806.01356] [INSPIRE].
A. Amariti, SUSY Breaking in Monopole Quivers, arXiv:1808.09983 [INSPIRE].
F. Aprile, S. Pasquetti and Y. Zenkevich, Flipping the head of T[SU(N)]: mirror symmetry, spectral duality and monopoles, arXiv:1812.08142 [INSPIRE].
A. Amariti, L. Cassia, I. Garozzo and N. Mekareeya, Branes, partition functions and quadratic monopole superpotentials, arXiv:1901.07559 [INSPIRE].
S. Benvenuti and S. Giacomelli, Abelianization and sequential confinement in 2 + 1 dimensions, JHEP 10 (2017) 173 [arXiv:1706.04949] [INSPIRE].
S. Benvenuti, A tale of exceptional 3d dualities, arXiv:1809.03925 [INSPIRE].
A. Amariti and L. Cassia, USp(2N c) SQCD 3 with antisymmetric: dualities and symmetry enhancements, JHEP 02 (2019) 013 [arXiv:1809.03796] [INSPIRE].
D. Gaiotto and E. Witten, S-duality of Boundary Conditions In N = 4 Super Yang-Mills Theory, Adv. Theor. Math. Phys. 13 (2009) 721 [arXiv:0807.3720] [INSPIRE].
N. Seiberg and E. Witten, Gauge dynamics and compactification to three-dimensions, in The mathematical beauty of physics: A memorial volume for Claude Itzykson. Proceedings, Conference, Saclay, France, June 5–7, 1996, pp. 333–366, 1996, hep-th/9607163 [INSPIRE].
B. Assel and S. Cremonesi, The Infrared Physics of Bad Theories, SciPost Phys. 3 (2017) 024 [arXiv:1707.03403] [INSPIRE].
A. Dey and P. Koroteev, Good IR Duals of Bad Quiver Theories, JHEP 05 (2018) 114 [arXiv:1712.06068] [INSPIRE].
B. Assel and S. Cremonesi, The Infrared Fixed Points of 3d \( \mathcal{N} \) = 4 USp(2N) SQCD Theories, SciPost Phys. 5 (2018) 015 [arXiv:1802.04285] [INSPIRE].
D. Jafferis and X. Yin, A Duality Appetizer, arXiv:1103.5700 [INSPIRE].
P. Agarwal, I. Bah, K. Maruyoshi and J. Song, Quiver tails and \( \mathcal{N} \) = 1 SCFTs from M5-branes, JHEP 03 (2015) 049 [arXiv:1409.1908] [INSPIRE].
S. Benvenuti and S. Giacomelli, Supersymmetric gauge theories with decoupled operators and chiral ring stability, Phys. Rev. Lett. 119 (2017) 251601 [arXiv:1706.02225] [INSPIRE].
N. Hama, K. Hosomichi and S. Lee, Notes on SUSY Gauge Theories on Three-Sphere, JHEP 03 (2011) 127 [arXiv:1012.3512] [INSPIRE].
N. Hama, K. Hosomichi and S. Lee, SUSY Gauge Theories on Squashed Three-Spheres, JHEP 05 (2011) 014 [arXiv:1102.4716] [INSPIRE].
M. Bullimore, H.-C. Kim and P. Koroteev, Defects and Quantum Seiberg-Witten Geometry, JHEP 05 (2015) 095 [arXiv:1412.6081] [INSPIRE].
D.L. Jafferis, The Exact Superconformal R-Symmetry Extremizes Z, JHEP 05 (2012) 159 [arXiv:1012.3210] [INSPIRE].
S. Cremonesi, A. Hanany, N. Mekareeya and A. Zaffaroni, Coulomb branch Hilbert series and Hall-Littlewood polynomials, JHEP 09 (2014) 178 [arXiv:1403.0585] [INSPIRE].
E. Witten, SL(2, ℤ) action on three-dimensional conformal field theories with Abelian symmetry, hep-th/0307041 [INSPIRE].
S. Cremonesi, A. Hanany and A. Zaffaroni, Monopole operators and Hilbert series of Coulomb branches of 3d \( \mathcal{N} \) = 4 gauge theories, JHEP 01 (2014) 005 [arXiv:1309.2657] [INSPIRE].
T. Dimofte, D. Gaiotto and N.M. Paquette, Dual boundary conditions in 3d SCFT’s, JHEP 05 (2018) 060 [arXiv:1712.07654] [INSPIRE].
S. Benvenuti and S. Giacomelli, Lagrangians for generalized Argyres-Douglas theories, JHEP 10 (2017) 106 [arXiv:1707.05113] [INSPIRE].
A. Giveon and D. Kutasov, Seiberg Duality in Chern-Simons Theory, Nucl. Phys. B 812 (2009) 1 [arXiv:0808.0360] [INSPIRE].
F. Benini, C. Closset and S. Cremonesi, Comments on 3d Seiberg-like dualities, JHEP 10 (2011) 075 [arXiv:1108.5373] [INSPIRE].
Y. Tachikawa, A review of the T N theory and its cousins, PTEP 2015 (2015) 11B102 [arXiv:1504.01481] [INSPIRE].
G. Ferlito and A. Hanany, A tale of two cones: the Higgs Branch of Sp(n) theories with 2n flavours, arXiv:1609.06724 [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].
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Giacomelli, S. Dualities for adjoint SQCD in three dimensions and emergent symmetries. J. High Energ. Phys. 2019, 144 (2019). https://doi.org/10.1007/JHEP03(2019)144
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DOI: https://doi.org/10.1007/JHEP03(2019)144