Abstract
We propose that a certain 4d \( \mathcal{N} \) = 1 SU(2) × SU(2) gauge theory flows in the IR to an \( \mathcal{N} \) = 3 SCFT plus a single free chiral field. The specific \( \mathcal{N} \) = 3 SCFT has rank 1 and a dimension three Coulomb branch operator. The flow is generically expected to land at the \( \mathcal{N} \) = 3 SCFT deformed by the marginal deformation associated with said Coulomb branch operator. We also present a discussion about the properties expected of various RG invariant quantities from \( \mathcal{N} \) = 3 superconformal symmetry, and use these to test our proposal. Finally, we discuss a generalization to another \( \mathcal{N} \) = 1 model that we propose is related to a certain rank 3 \( \mathcal{N} \) = 3 SCFT through the turning of certain marginal deformations.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
I. García-Etxebarria and D. Regalado, \( \mathcal{N} \) = 3 four dimensional field theories, JHEP 03 (2016) 083 [arXiv:1512.06434] [INSPIRE].
O. Aharony and Y. Tachikawa, S-folds and 4d \( \mathcal{N} \) = 3 superconformal field theories, JHEP 06 (2016) 044 [arXiv:1602.08638] [INSPIRE].
I. García-Etxebarria and D. Regalado, Exceptional \( \mathcal{N} \) = 3 theories, JHEP 12 (2017) 042 [arXiv:1611.05769] [INSPIRE].
J.A. Minahan and D. Nemeschansky, An N = 2 superconformal fixed point with E6 global symmetry, Nucl. Phys. B 482 (1996) 142 [hep-th/9608047] [INSPIRE].
P.C. Argyres and J.R. Wittig, Infinite coupling duals of N = 2 gauge theories and new rank 1 superconformal field theories, JHEP 01 (2008) 074 [arXiv:0712.2028] [INSPIRE].
D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].
O. Chacaltana and J. Distler, Tinkertoys for Gaiotto Duality, JHEP 11 (2010) 099 [arXiv:1008.5203] [INSPIRE].
O. Chacaltana and J. Distler, Tinkertoys for the DN series, JHEP 02 (2013) 110 [arXiv:1106.5410] [INSPIRE].
P.C. Argyres and N. Seiberg, S-duality in N = 2 supersymmetric gauge theories, JHEP 12 (2007) 088 [arXiv:0711.0054] [INSPIRE].
P.C. Argyres and M.R. Douglas, New phenomena in SU(3) supersymmetric gauge theory, Nucl. Phys. B 488 (1995) 93 [hep-th/9505062] [INSPIRE].
P.C. Argyres, M. Plesser, N. Seiberg and E. Witten, New N = 2 superconformal field theories in four-dimensions, Nucl. Phys. B 461 (1996) 71 [hep-th/9511154] [INSPIRE].
P.C. Argyres, M. Lotito, Y. Lü and M. Martone, Expanding the landscape of \( \mathcal{N} \) = 2 rank 1 SCFTs, JHEP 05 (2016) 088 [arXiv:1602.02764] [INSPIRE].
G. Zafrir, Compactifications of 5d SCFTs with a twist, JHEP 01 (2017) 097 [arXiv:1605.08337] [INSPIRE].
R.G. Leigh and M.J. Strassler, Exactly marginal operators and duality in four-dimensional N = 1 supersymmetric gauge theory, Nucl. Phys. B 447 (1995) 95 [hep-th/9503121] [INSPIRE].
D. Green, Z. Komargodski, N. Seiberg, Y. Tachikawa and B. Wecht, Exactly Marginal Deformations and Global Symmetries, JHEP 06 (2010) 106 [arXiv:1005.3546] [INSPIRE].
S.S. Razamat, E. Sabag and G. Zafrir, Weakly coupled conformal manifolds in 4d, JHEP 06 (2020) 179 [arXiv:2004.07097] [INSPIRE].
S.S. Razamat and G. Zafrir, N = 1 conformal dualities, JHEP 09 (2019) 046 [arXiv:1906.05088] [INSPIRE].
K. Maruyoshi and J. Song, Enhancement of Supersymmetry via Renormalization Group Flow and the Superconformal Index, Phys. Rev. Lett. 118 (2017) 151602 [arXiv:1606.05632] [INSPIRE].
K. Maruyoshi and J. Song, \( \mathcal{N} \) = 1 deformations and RG flows of \( \mathcal{N} \) = 2 SCFTs, JHEP 02 (2017) 075 [arXiv:1607.04281] [INSPIRE].
P. Agarwal, K. Maruyoshi and J. Song, \( \mathcal{N} \) = 1 Deformations and RG flows of \( \mathcal{N} \) = 2 SCFTs, part II: Non-principal deformations, JHEP 12 (2016) 103 [Addendum ibid. 04 (2017) 113] [arXiv:1610.05311] [INSPIRE].
P. Agarwal, A. Sciarappa and J. Song, \( \mathcal{N} \) = 1 Lagrangians for generalized Argyres-Douglas theories, JHEP 10 (2017) 211 [arXiv:1707.04751] [INSPIRE].
S. Benvenuti and S. Giacomelli, Lagrangians for generalized Argyres-Douglas theories, JHEP 10 (2017) 106 [arXiv:1707.05113] [INSPIRE].
K. Maruyoshi, E. Nardoni and J. Song, Landscape of Simple Superconformal Field Theories in 4d, Phys. Rev. Lett. 122 (2019) 121601 [arXiv:1806.08353] [INSPIRE].
A. Gadde, S.S. Razamat and B. Willett, “Lagrangian” for a Non-Lagrangian Field Theory with \( \mathcal{N} \) = 2 Supersymmetry, Phys. Rev. Lett. 115 (2015) 171604 [arXiv:1505.05834] [INSPIRE].
P. Agarwal, K. Maruyoshi and J. Song, A “Lagrangian” for the E7 superconformal theory, JHEP 05 (2018) 193 [arXiv:1802.05268] [INSPIRE].
G. Zafrir, An \( \mathcal{N} \) = 1 Lagrangian for the rank 1 E6 superconformal theory, JHEP 12 (2020) 098 [arXiv:1912.09348] [INSPIRE].
T. Nishinaka and Y. Tachikawa, On 4d rank-one \( \mathcal{N} \) = 3 superconformal field theories, JHEP 09 (2016) 116 [arXiv:1602.01503] [INSPIRE].
Y. Imamura and S. Yokoyama, Superconformal index of \( \mathcal{N} \) = 3 orientifold theories, J. Phys. A 49 (2016) 435401 [arXiv:1603.00851] [INSPIRE].
R. Arai and Y. Imamura, Finite N Corrections to the Superconformal Index of S-fold Theories, PTEP 2019 (2019) 083B04 [arXiv:1904.09776] [INSPIRE].
M. Evtikhiev, Studying superconformal symmetry enhancement through indices, JHEP 04 (2018) 120 [arXiv:1708.08307] [INSPIRE].
M. Caorsi and S. Cecotti, Geometric classification of 4d \( \mathcal{N} \) = 2 SCFTs, JHEP 07 (2018) 138 [arXiv:1801.04542] [INSPIRE].
F. Bonetti, C. Meneghelli and L. Rastelli, VOAs labelled by complex reflection groups and 4d SCFTs, JHEP 05 (2019) 155 [arXiv:1810.03612] [INSPIRE].
Y. Tachikawa and G. Zafrir, Reflection groups and 3d \( \mathcal{N} \) ≥ 6 SCFTs, JHEP 12 (2019) 176 [arXiv:1908.03346] [INSPIRE].
P.C. Argyres, A. Bourget and M. Martone, Classification of all \( \mathcal{N} \) ≥ 3 moduli space orbifold geometries at rank 2, SciPost Phys. 9 (2020) 083 [arXiv:1904.10969] [INSPIRE].
P.C. Argyres, A. Bourget and M. Martone, On the moduli spaces of 4d \( \mathcal{N} \) = 3 SCFTs I: triple special Kähler structure, arXiv:1912.04926 [INSPIRE].
C. Cordova, T.T. Dumitrescu and K. Intriligator, Multiplets of Superconformal Symmetry in Diverse Dimensions, JHEP 03 (2019) 163 [arXiv:1612.00809] [INSPIRE].
M. Lemos, P. Liendo, C. Meneghelli and V. Mitev, Bootstrapping \( \mathcal{N} \) = 3 superconformal theories, JHEP 04 (2017) 032 [arXiv:1612.01536] [INSPIRE].
T. Bourton, A. Pini and E. Pomoni, 4d \( \mathcal{N} \) = 3 indices via discrete gauging, JHEP 10 (2018) 131 [arXiv:1804.05396] [INSPIRE].
O. Aharony and M. Evtikhiev, On four dimensional N = 3 superconformal theories, JHEP 04 (2016) 040 [arXiv:1512.03524] [INSPIRE].
A.D. Shapere and Y. Tachikawa, Central charges of N = 2 superconformal field theories in four dimensions, JHEP 09 (2008) 109 [arXiv:0804.1957] [INSPIRE].
P.C. Argyres and M. Martone, 4d \( \mathcal{N} \) = 2 theories with disconnected gauge groups, JHEP 03 (2017) 145 [arXiv:1611.08602] [INSPIRE].
M. Evtikhiev, N = 3 SCFTs in 4 dimensions and non-simply laced groups, JHEP 06 (2020) 125 [arXiv:2004.03919] [INSPIRE].
P. Argyres, M. Lotito, Y. Lü and M. Martone, Geometric constraints on the space of \( \mathcal{N} \) = 2 SCFTs. Part I: physical constraints on relevant deformations, JHEP 02 (2018) 001 [arXiv:1505.04814] [INSPIRE].
P.C. Argyres, M. Lotito, Y. Lü and M. Martone, Geometric constraints on the space of \( \mathcal{N} \) = 2 SCFTs. Part II: construction of special Kähler geometries and RG flows, JHEP 02 (2018) 002 [arXiv:1601.00011] [INSPIRE].
P. Argyres, M. Lotito, Y. Lü and M. Martone, Geometric constraints on the space of \( \mathcal{N} \) = 2 SCFTs. Part III: enhanced Coulomb branches and central charges, JHEP 02 (2018) 003 [arXiv:1609.04404] [INSPIRE].
K.A. Intriligator and B. Wecht, The Exact superconformal R symmetry maximizes a, Nucl. Phys. B 667 (2003) 183 [hep-th/0304128] [INSPIRE].
D. Kutasov, A. Parnachev and D.A. Sahakyan, Central charges and U(1)(R) symmetries in N = 1 superYang-Mills, JHEP 11 (2003) 013 [hep-th/0308071] [INSPIRE].
J. Kinney, J.M. Maldacena, S. Minwalla and S. Raju, An Index for 4 dimensional super conformal theories, Commun. Math. Phys. 275 (2007) 209 [hep-th/0510251] [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].
F.A. Dolan and H. Osborn, Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N = 1 Dual Theories, Nucl. Phys. B 818 (2009) 137 [arXiv:0801.4947] [INSPIRE].
L. Rastelli and S.S. Razamat, The supersymmetric index in four dimensions, J. Phys. A 50 (2017) 443013 [arXiv:1608.02965] [INSPIRE].
A. Gadde, L. Rastelli, S.S. Razamat and W. Yan, Gauge Theories and Macdonald Polynomials, Commun. Math. Phys. 319 (2013) 147 [arXiv:1110.3740] [INSPIRE].
S.S. Razamat and G. Zafrir, \( \mathcal{N} \) = 1 conformal duals of gauged En MN models, JHEP 06 (2020) 176 [arXiv:2003.01843] [INSPIRE].
C. Beem, M. Lemos, P. Liendo, W. Peelaers, L. Rastelli and B.C. van Rees, Infinite Chiral Symmetry in Four Dimensions, Commun. Math. Phys. 336 (2015) 1359 [arXiv:1312.5344] [INSPIRE].
K.A. Intriligator, N. Seiberg and S.H. Shenker, Proposal for a simple model of dynamical SUSY breaking, Phys. Lett. B 342 (1995) 152 [hep-ph/9410203] [INSPIRE].
J.H. Brodie, P.L. Cho and K.A. Intriligator, Misleading anomaly matchings?, Phys. Lett. B 429 (1998) 319 [hep-th/9802092] [INSPIRE].
K.A. Intriligator, IR free or interacting? A Proposed diagnostic, Nucl. Phys. B 730 (2005) 239 [hep-th/0509085] [INSPIRE].
G.S. Vartanov, On the ISS model of dynamical SUSY breaking, Phys. Lett. B 696 (2011) 288 [arXiv:1009.2153] [INSPIRE].
Y. Tachikawa, Lectures on 4d N = 1 dynamics and related topics, arXiv:1812.08946 [INSPIRE].
N. Seiberg, Electric-magnetic duality in supersymmetric nonAbelian gauge theories, Nucl. Phys. B 435 (1995) 129 [hep-th/9411149] [INSPIRE].
A. Gadde, L. Rastelli, S.S. Razamat and W. Yan, The Superconformal Index of the E6 SCFT, JHEP 08 (2010) 107 [arXiv:1003.4244] [INSPIRE].
S.S. Razamat, C. Vafa and G. Zafrir, 4d \( \mathcal{N} \) = 1 from 6d (1, 0), JHEP 04 (2017) 064 [arXiv:1610.09178] [INSPIRE].
D. Gaiotto, A. Kapustin, N. Seiberg and B. Willett, Generalized Global Symmetries, JHEP 02 (2015) 172 [arXiv:1412.5148] [INSPIRE].
C. Beem and A. Gadde, The N = 1 superconformal index for class S fixed points, JHEP 04 (2014) 036 [arXiv:1212.1467] [INSPIRE].
A. Gadde, L. Rastelli, S.S. Razamat and W. Yan, The 4d Superconformal Index from q-deformed 2d Yang-Mills, Phys. Rev. Lett. 106 (2011) 241602 [arXiv:1104.3850] [INSPIRE].
F. Benini, Y. Tachikawa and B. Wecht, Sicilian gauge theories and N = 1 dualities, JHEP 01 (2010) 088 [arXiv:0909.1327] [INSPIRE].
S.M. Kuzenko and S. Theisen, Correlation functions of conserved currents in N = 2 superconformal theory, Class. Quant. Grav. 17 (2000) 665696 [hep-th/9907107] [INSPIRE].
H. Shimizu, Y. Tachikawa and G. Zafrir, Anomaly matching on the Higgs branch, JHEP 12 (2017) 127 [arXiv:1703.01013] [INSPIRE].
C. Cordova, T.T. Dumitrescu and K. Intriligator, Deformations of Superconformal Theories, JHEP 11 (2016) 135 [arXiv:1602.01217] [INSPIRE].
M. Buican, T. Nishinaka and C. Papageorgakis, Constraints on chiral operators in \( \mathcal{N} \) = 2 SCFTs, JHEP 12 (2014) 095 [arXiv:1407.2835] [INSPIRE].
A. Manenti, Differential operators for superconformal correlation functions, JHEP 20 (2020) 145 [arXiv:1910.12869] [INSPIRE].
A. Gadde, L. Rastelli, S.S. Razamat and W. Yan, On the Superconformal Index of N = 1 IR Fixed Points: A Holographic Check, JHEP 03 (2011) 041 [arXiv:1011.5278] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2007.14955
Rights and permissions
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.
About this article
Cite this article
Zafrir, G. An \( \mathcal{N} \) = 1 Lagrangian for an \( \mathcal{N} \) = 3 SCFT. J. High Energ. Phys. 2021, 62 (2021). https://doi.org/10.1007/JHEP01(2021)062
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2021)062