Abstract
We study 3d theories containing \( \mathcal{N} \) = 3 Chern-Simons vector multiplets coupled to the SU(N)3 flavour symmetry of 3d TN theories with Chern-Simons levels k1, k2 and k3. It was formerly pointed out that these theories flow to infrared SCFTs with enhanced \( \mathcal{N} \) = 4 supersymmetry when 1/k1 + 1/k2 + 1/k3 = 0. We examine superconformal indices of these theories which reveal that supersymmetry of the infrared SCFTs may get enhanced to 4 ≤ \( \mathcal{N} \) ≤ 6 if such a condition is satisfied. Moreover, even if the Chern-Simons levels do not obey the aforementioned condition, we find that there is still an infinite family of theories that flows to infrared SCFTs with \( \mathcal{N} \) = 4 supersymmetry. The ’t Hooft anomalies of the one-form symmetries of these theories are analysed. As a by-product, we observe that there is generally a decoupled topological sector in the infrared. When the infrared SCFTs have \( \mathcal{N} \) ≥ 4 supersymmetry, we also study the Higgs and Coulomb branch limits of the indices which provide geometric information of the moduli space of the theories in question in terms of the Hilbert series.
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References
D. Gaiotto and X. Yin, Notes on superconformal Chern-Simons-Matter theories, JHEP 08 (2007) 056 [arXiv:0704.3740] [INSPIRE].
A. Gustavsson, Algebraic structures on parallel M2-branes, Nucl. Phys. B 811 (2009) 66 [arXiv:0709.1260] [INSPIRE].
J. Bagger and N. Lambert, Gauge symmetry and supersymmetry of multiple M2-branes, Phys. Rev. D 77 (2008) 065008 [arXiv:0711.0955] [INSPIRE].
M.A. Bandres, A.E. Lipstein and J.H. Schwarz, N = 8 Superconformal Chern-Simons Theories, JHEP 05 (2008) 025 [arXiv:0803.3242] [INSPIRE].
D. Gaiotto and E. Witten, Janus Configurations, Chern-Simons Couplings, And The theta-Angle in N=4 Super Yang-Mills Theory, JHEP 06 (2010) 097 [arXiv:0804.2907] [INSPIRE].
K. Hosomichi et al., N=4 Superconformal Chern-Simons Theories with Hyper and Twisted Hyper Multiplets, JHEP 07 (2008) 091 [arXiv:0805.3662] [INSPIRE].
K. Hosomichi et al., N=5,6 Superconformal Chern-Simons Theories and M2-branes on Orbifolds, JHEP 09 (2008) 002 [arXiv:0806.4977] [INSPIRE].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
M. Schnabl and Y. Tachikawa, Classification of N=6 superconformal theories of ABJM type, JHEP 09 (2010) 103 [arXiv:0807.1102] [INSPIRE].
O. Aharony, O. Bergman and D.L. Jafferis, Fractional M2-branes, JHEP 11 (2008) 043 [arXiv:0807.4924] [INSPIRE].
D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].
D. Gaiotto and J. Maldacena, The gravity duals of N = 2 superconformal field theories, JHEP 10 (2012) 189 [arXiv:0904.4466] [INSPIRE].
J. Eckhard, H. Kim, S. Schafer-Nameki and B. Willett, Higher-Form Symmetries, Bethe Vacua, and the 3d-3d Correspondence, JHEP 01 (2020) 101 [arXiv:1910.14086] [INSPIRE].
B. Assel, Y. Tachikawa and A. Tomasiello, On \( \mathcal{N} \) = 4 supersymmetry enhancements in three dimensions, JHEP 03 (2023) 170 [arXiv:2209.13984] [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].
A. Gadde, S. Gukov and P. Putrov, Fivebranes and 4-manifolds, Prog. Math. 319 (2016) 155 [arXiv:1306.4320] [INSPIRE].
H.-J. Chung, T. Dimofte, S. Gukov and P. Sułkowski, 3d-3d Correspondence Revisited, JHEP 04 (2016) 140 [arXiv:1405.3663] [INSPIRE].
S. Gukov, P. Putrov and C. Vafa, Fivebranes and 3-manifold homology, JHEP 07 (2017) 071 [arXiv:1602.05302] [INSPIRE].
S. Gukov, D. Pei, P. Putrov and C. Vafa, BPS spectra and 3-manifold invariants, J. Knot Theor. Ramifications 29 (2020) 2040003 [arXiv:1701.06567] [INSPIRE].
D. Gang and K. Yonekura, Symmetry enhancement and closing of knots in 3d/3d correspondence, JHEP 07 (2018) 145 [arXiv:1803.04009] [INSPIRE].
B. Assel and A. Tomasiello, Holographic duals of 3d S-fold CFTs, JHEP 06 (2018) 019 [arXiv:1804.06419] [INSPIRE].
D. Gang and M. Yamazaki, Three-dimensional gauge theories with supersymmetry enhancement, Phys. Rev. D 98 (2018) 121701 [arXiv:1806.07714] [INSPIRE].
G.Y. Cho, D. Gang and H.-C. Kim, M-theoretic Genesis of Topological Phases, JHEP 11 (2020) 115 [arXiv:2007.01532] [INSPIRE].
D. Gang et al., Non-unitary TQFTs from 3D \( \mathcal{N} \) = 4 rank 0 SCFTs, JHEP 08 (2021) 158 [arXiv:2103.09283] [INSPIRE].
J. Bhattacharya, S. Bhattacharyya, S. Minwalla and S. Raju, Indices for Superconformal Field Theories in 3, 5 and 6 Dimensions, JHEP 02 (2008) 064 [arXiv:0801.1435] [INSPIRE].
J. Bhattacharya and S. Minwalla, Superconformal Indices for N = 6 Chern Simons Theories, JHEP 01 (2009) 014 [arXiv:0806.3251] [INSPIRE].
S. Kim, The complete superconformal index for N = 6 Chern-Simons theory, Nucl. Phys. B 821 (2009) 241 [Erratum ibid. 864 (2012) 884] [arXiv:0903.4172] [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].
A. Kapustin and B. Willett, Generalized Superconformal Index for Three Dimensional Field Theories, arXiv:1106.2484 [INSPIRE].
T. Dimofte, D. Gaiotto and S. Gukov, 3-Manifolds and 3d Indices, Adv. Theor. Math. Phys. 17 (2013) 975 [arXiv:1112.5179] [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].
I. Garozzo, G. Lo Monaco, N. Mekareeya and M. Sacchi, Supersymmetric Indices of 3d S-fold SCFTs, JHEP 08 (2019) 008 [arXiv:1905.07183] [INSPIRE].
E. Beratto, N. Mekareeya and M. Sacchi, Zero-form and one-form symmetries of the ABJ and related theories, JHEP 04 (2022) 126 [arXiv:2112.09531] [INSPIRE].
N. Mekareeya and M. Sacchi, Mixed anomalies, two-groups, non-invertible symmetries, and 3d superconformal indices, JHEP 01 (2023) 115 [arXiv:2210.02466] [INSPIRE].
A. Kapustin and N. Seiberg, Coupling a QFT to a TQFT and Duality, JHEP 04 (2014) 001 [arXiv:1401.0740] [INSPIRE].
D. Gaiotto, A. Kapustin, N. Seiberg and B. Willett, Generalized Global Symmetries, JHEP 02 (2015) 172 [arXiv:1412.5148] [INSPIRE].
P.-S. Hsin, H.T. Lam and N. Seiberg, Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d, SciPost Phys. 6 (2019) 039 [arXiv:1812.04716] [INSPIRE].
M. Sacchi, O. Sela and G. Zafrir, 5d to 3d compactifications and discrete anomalies, arXiv:2305.08185 [INSPIRE].
S.S. Razamat and B. Willett, Down the rabbit hole with theories of class , JHEP 10 (2014) 099 [arXiv:1403.6107] [INSPIRE].
S. Benvenuti, B. Feng, A. Hanany and Y.-H. He, Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics, JHEP 11 (2007) 050 [hep-th/0608050] [INSPIRE].
B. Feng, A. Hanany and Y.-H. He, Counting gauge invariants: The plethystic program, JHEP 03 (2007) 090 [hep-th/0701063] [INSPIRE].
B. Li, D. Xie and W.B. Yan, Superconformal indices of \( \mathcal{N} \) = 4 Chern-Simons matter theories, arXiv:2305.08784 [INSPIRE].
L. Bhardwaj, Global form of flavor symmetry groups in 4d N = 2 theories of class S, SciPost Phys. 12 (2022) 183 [arXiv:2105.08730] [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].
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].
C. Cordova, T.T. Dumitrescu and K. Intriligator, Multiplets of Superconformal Symmetry in Diverse Dimensions, JHEP 03 (2019) 163 [arXiv:1612.00809] [INSPIRE].
S.S. Razamat and G. Zafrir, Exceptionally simple exceptional models, JHEP 11 (2016) 061 [arXiv:1609.02089] [INSPIRE].
M. Evtikhiev, Studying superconformal symmetry enhancement through indices, JHEP 04 (2018) 120 [arXiv:1708.08307] [INSPIRE].
E. Beratto, N. Mekareeya and M. Sacchi, Marginal operators and supersymmetry enhancement in 3d S-fold SCFTs, JHEP 12 (2020) 017 [arXiv:2009.10123] [INSPIRE].
Y. Tachikawa and G. Zafrir, Reflection groups and 3d \( \mathcal{N} \) ≥ 6 SCFTs, JHEP 12 (2019) 176 [arXiv:1908.03346] [INSPIRE].
Y. Tachikawa, On gauging finite subgroups, SciPost Phys. 8 (2020) 015 [arXiv:1712.09542] [INSPIRE].
N. Seiberg and E. Witten, Gauge dynamics and compactification to three-dimensions, in the proceedings of the Conference on the Mathematical Beauty of Physics (In Memory of C. Itzykson), Saclay, France, June 5–7, 1996, p. 333–366 [hep-th/9607163] [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].
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].
A. Hatcher, Notes on basic 3-manifold topology, (2007) https://pi.math.cornell.edu/~hatcher/3M/3M.pdf.
P.B. Genolini and L. Tizzano, Comments on Global Symmetries and Anomalies of 5d SCFTs, arXiv:2201.02190 [INSPIRE].
L. Bhardwaj, M. Bullimore, A.E.V. Ferrari and S. Schafer-Nameki, Anomalies of Generalized Symmetries from Solitonic Defects, arXiv:2205.15330 [INSPIRE].
Z. Komargodski, A. Sharon, R. Thorngren and X. Zhou, Comments on Abelian Higgs Models and Persistent Order, SciPost Phys. 6 (2019) 003 [arXiv:1705.04786] [INSPIRE].
L. Bhardwaj, M. Hubner and S. Schafer-Nameki, 1-form Symmetries of 4d N = 2 Class S Theories, SciPost Phys. 11 (2021) 096 [arXiv:2102.01693] [INSPIRE].
O. Bergman, Y. Tachikawa and G. Zafrir, Generalized symmetries and holography in ABJM-type theories, JHEP 07 (2020) 077 [arXiv:2004.05350] [INSPIRE].
K. Maruyoshi, Y. Tachikawa, W. Yan and K. Yonekura, \( \mathcal{N} \) = 1 dynamics with TN theory, JHEP 10 (2013) 010 [arXiv:1305.5250] [INSPIRE].
Y. Tachikawa, A review of the TN theory and its cousins, PTEP 2015 (2015) 11B102 [arXiv:1504.01481] [INSPIRE].
L. Bhardwaj, M. Bullimore, A.E.V. Ferrari and S. Schafer-Nameki, Generalized Symmetries and Anomalies of 3d N = 4 SCFTs, arXiv:2301.02249 [INSPIRE].
Acknowledgments
We express our gratitude to Matteo Sacchi and Alessandro Tomasiello for a number of useful discussions and for carefully reading through the manuscript as well as providing us with insightful comments. N.M. thanks the visiting research fellowship of the CNRS and the LPTENS, ENS Paris, where part of this project was conducted.
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Comi, R., Harding, W. & Mekareeya, N. Chern-Simons-Trinion theories: One-form symmetries and superconformal indices. J. High Energ. Phys. 2023, 60 (2023). https://doi.org/10.1007/JHEP09(2023)060
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DOI: https://doi.org/10.1007/JHEP09(2023)060