Abstract
One interesting feature of 3d \( \mathcal{N} \) = 2 theories is that gauge-invariant operators can decouple by strong-coupling effects, leading to emergent flavor symmetries in the IR. The details of such decoupling, however, depends very delicately on the gauge group and matter content of the theory. We here systematically study the IR behavior of 3d \( \mathcal{N} \) = 2 SQCD with N f flavors, for gauge groups SU(N c ), USp(2N c ) and SO(N c ). We apply a combination of analytical and numerical methods, both to small values of N c , N f and also to the Veneziano limit, where N c and N f are taken to be large with their ratio N f /N c fixed. We highlight the role of monopole operators and their interplay with Aharony-type dualities. We also discuss the effect of gauging continuous and discrete flavor symmetries, and the implications of our analysis to the classification of 1/4-BPS co-dimension 2 defects of 6d (2, 0) theories.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
I. Affleck, J.A. Harvey and E. Witten, Instantons and (super)symmetry breaking in (2 + 1)-dimensions, Nucl. Phys. B 206 (1982) 413 [INSPIRE].
D. Kutasov, A comment on duality in N = 1 supersymmetric non-Abelian gauge theories, Phys. Lett. B 351 (1995) 230 [hep-th/9503086] [INSPIRE].
D. Kutasov and A. Schwimmer, On duality in supersymmetric Yang-Mills theory, Phys. Lett. B 354 (1995) 315 [hep-th/9505004] [INSPIRE].
B.R. Safdi, I.R. Klebanov and J. Lee, A crack in the conformal window, JHEP 04 (2013) 165 [arXiv:1212.4502] [INSPIRE].
G. Mack, All unitary ray representations of the conformal group SU(2, 2) with positive energy, Commun. Math. Phys. 55 (1977) 1 [INSPIRE].
M. Flato and C. Fronsdal, Representations of conformal supersymmetry, Lett. Math. Phys. 8 (1984) 159 [INSPIRE].
V.K. Dobrev and V.B. Petkova, All positive energy unitary irreducible representations of extended conformal supersymmetry, Phys. Lett. B 162 (1985) 127 [INSPIRE].
S. Minwalla, Restrictions imposed by superconformal invariance on quantum field theories, Adv. Theor. Math. Phys. 2 (1998) 781 [hep-th/9712074] [INSPIRE].
J. Penedones, E. Trevisani and M. Yamazaki, Recursion relations for conformal blocks, arXiv:1509.00428 [INSPIRE].
M. Yamazaki, Comments on determinant formulas for general CFTs, arXiv:1601.04072 [INSPIRE].
V. Borokhov, A. Kapustin and X.-K. Wu, Monopole operators and mirror symmetry in three-dimensions, JHEP 12 (2002) 044 [hep-th/0207074] [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].
D.L. Jafferis, The exact superconformal R-symmetry extremizes Z, JHEP 05 (2012) 159 [arXiv:1012.3210] [INSPIRE].
C. Closset, T.T. Dumitrescu, G. Festuccia, Z. Komargodski and N. Seiberg, Comments on Chern-Simons contact terms in three dimensions, JHEP 09 (2012) 091 [arXiv:1206.5218] [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].
N. Hama, K. Hosomichi and S. Lee, Notes on SUSY gauge theories on three-sphere, JHEP 03 (2011) 127 [arXiv:1012.3512] [INSPIRE].
V. Niarchos, Comments on F-maximization and R-symmetry in 3D SCFTs, J. Phys. A 44 (2011) 305404 [arXiv:1103.5909] [INSPIRE].
T. Morita and V. Niarchos, F-theorem, duality and SUSY breaking in one-adjoint Chern-Simons-matter theories, Nucl. Phys. B 858 (2012) 84 [arXiv:1108.4963] [INSPIRE].
P. Agarwal, A. Amariti and M. Siani, Refined checks and exact dualities in three dimensions, JHEP 10 (2012) 178 [arXiv:1205.6798] [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].
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].
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].
F.A.H. Dolan, V.P. Spiridonov and G.S. Vartanov, From 4d superconformal indices to 3d partition functions, Phys. Lett. B 704 (2011) 234 [arXiv:1104.1787] [INSPIRE].
B. Willett and I. Yaakov, N = 2 dualities and Z extremization in three dimensions, arXiv:1104.0487 [INSPIRE].
D. Bashkirov, Aharony duality and monopole operators in three dimensions, arXiv:1106.4110 [INSPIRE].
F. Benini, C. Closset and S. Cremonesi, Comments on 3d Seiberg-like dualities, JHEP 10 (2011) 075 [arXiv:1108.5373] [INSPIRE].
G. Festuccia and N. Seiberg, Rigid supersymmetric theories in curved superspace, JHEP 06 (2011) 114 [arXiv:1105.0689] [INSPIRE].
R.C. Myers and A. Sinha, Seeing a c-theorem with holography, Phys. Rev. D 82 (2010) 046006 [arXiv:1006.1263] [INSPIRE].
D.L. Jafferis, I.R. Klebanov, S.S. Pufu and B.R. Safdi, Towards the F-theorem: N = 2 field theories on the three-sphere, JHEP 06 (2011) 102 [arXiv:1103.1181] [INSPIRE].
I.R. Klebanov, S.S. Pufu and B.R. Safdi, F-theorem without supersymmetry, JHEP 10 (2011) 038 [arXiv:1105.4598] [INSPIRE].
H. Casini and M. Huerta, On the RG running of the entanglement entropy of a circle, Phys. Rev. D 85 (2012) 125016 [arXiv:1202.5650] [INSPIRE].
I.R. Klebanov, S.S. Pufu, S. Sachdev and B.R. Safdi, Entanglement entropy of 3D conformal gauge theories with many flavors, JHEP 05 (2012) 036 [arXiv:1112.5342] [INSPIRE].
I. Yaakov, Redeeming bad theories, JHEP 11 (2013) 189 [arXiv:1303.2769] [INSPIRE].
A. Karch, Seiberg duality in three-dimensions, Phys. Lett. B 405 (1997) 79 [hep-th/9703172] [INSPIRE].
C. Hwang, K.-J. Park and J. Park, Evidence for Aharony duality for orthogonal gauge groups, JHEP 11 (2011) 011 [arXiv:1109.2828] [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].
Y.-H. He, On algebraic singularities, finite graphs and D-brane gauge theories: a string theoretic perspective, hep-th/0209230 [INSPIRE].
M. Yamazaki, Brane tilings and their applications, Fortsch. Phys. 56 (2008) 555 [arXiv:0803.4474] [INSPIRE].
M. Yamazaki, Entanglement in theory space, Europhys. Lett. 103 (2013) 21002 [arXiv:1304.0762] [INSPIRE].
M. Yamazaki, Quivers, YBE and 3-manifolds, JHEP 05 (2012) 147 [arXiv:1203.5784] [INSPIRE].
Y. Terashima and M. Yamazaki, Emergent 3-manifolds from 4d superconformal indices, Phys. Rev. Lett. 109 (2012) 091602 [arXiv:1203.5792] [INSPIRE].
W. Cottrell, J. Hanson and A. Hashimoto, Dynamics of N = 4 supersymmetric field theories in 2 + 1 dimensions and their gravity dual, arXiv:1509.04749 [INSPIRE].
W. Cottrell and A. Hashimoto, Resolved gravity duals of N = 4 quiver field theories in 2 + 1 dimensions, arXiv:1602.04765 [INSPIRE].
A. Hashimoto, P. Ouyang and M. Yamazaki, Boundaries and defects of N = 4 SYM with 4 supercharges. Part I: boundary/junction conditions, JHEP 10 (2014) 107 [arXiv:1404.5527] [INSPIRE].
A. Hashimoto, P. Ouyang and M. Yamazaki, Boundaries and defects of N = 4 SYM with 4 supercharges. Part II: brane constructions and 3d N = 2 field theories, JHEP 10 (2014) 108 [arXiv:1406.5501] [INSPIRE].
G. Bonelli, S. Giacomelli, K. Maruyoshi and A. Tanzini, N = 1 geometries via M-theory, JHEP 10 (2013) 227 [arXiv:1307.7703] [INSPIRE].
D. Xie, M 5 brane and four dimensional N = 1 theories I, JHEP 04 (2014) 154 [arXiv:1307.5877] [INSPIRE].
D. Gang, N. Kim, M. Romo and M. Yamazaki, Aspects of defects in 3d-3d correspondence, arXiv:1510.05011 [INSPIRE].
K. Yonekura, Supersymmetric gauge theory, (2, 0) theory and twisted 5d super-Yang-Mills, JHEP 01 (2014) 142 [arXiv:1310.7943] [INSPIRE].
M. Bullimore and H.-C. Kim, The superconformal index of the (2, 0) theory with defects, JHEP 05 (2015) 048 [arXiv:1412.3872] [INSPIRE].
M. Bullimore, H.-C. Kim and P. Koroteev, Defects and quantum Seiberg-Witten geometry, JHEP 05 (2015) 095 [arXiv:1412.6081] [INSPIRE].
D. Gang, N. Kim, M. Romo and M. Yamazaki, Taming supersymmetric defects in 3d-3d correspondence, arXiv:1510.03884 [INSPIRE].
D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].
N. Wyllard, A N −1 conformal Toda field theory correlation functions from conformal N = 2 SU(N ) quiver gauge theories, JHEP 11 (2009) 002 [arXiv:0907.2189] [INSPIRE].
Y. Terashima and M. Yamazaki, SL(2, R) Chern-Simons, Liouville and gauge theory on duality walls, JHEP 08 (2011) 135 [arXiv:1103.5748] [INSPIRE].
T. Dimofte, D. Gaiotto and S. Gukov, Gauge theories labelled by three-manifolds, Commun. Math. Phys. 325 (2014) 367 [arXiv:1108.4389] [INSPIRE].
S. Lee and M. Yamazaki, 3d Chern-Simons theory from M 5-branes, JHEP 12 (2013) 035 [arXiv:1305.2429] [INSPIRE].
C. Cordova and D.L. Jafferis, Complex Chern-Simons from M 5-branes on the squashed three-sphere, arXiv:1305.2891 [INSPIRE].
E. Witten, SL(2, Z) action on three-dimensional conformal field theories with Abelian symmetry, hep-th/0307041 [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: 1603.02283
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
Lee, J., Yamazaki, M. Gauging and decoupling in 3d \( \mathcal{N} \) = 2 dualities. J. High Energ. Phys. 2016, 77 (2016). https://doi.org/10.1007/JHEP06(2016)077
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2016)077