Abstract
We propose that a certain 4d \( \mathcal{N} \) = 1 SU(4) gauge theory flows in the IR to the rank 1 \( \mathcal{N} \) = 2 strongly coupled SCFT with E6 global symmetry and 25 free chiral fields. This proposal is tested by comparing various RG invariant quantities, notably, anomalies and the superconformal index. We discuss the generalization to \( \mathcal{N} \) = 1 SU(2n + 2) gauge theory models flowing in the IR to the R(2,2n+1) family of strongly coupled SCFTs plus free fields.
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References
L. Bhardwaj and Y. Tachikawa, Classification of 4d N = 2 gauge theories, JHEP 12 (2013) 100 [arXiv:1309.5160] [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].
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].
J.A. Minahan and D. Nemeschansky, Superconformal fixed points with En global symmetry, Nucl. Phys. B 489 (1997) 24 [hep-th/9610076] [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].
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].
S.S. Razamat, C. Vafa and G. Zafrir, 4d \( \mathcal{N} \) = 1 from 6d (1, 0), JHEP 04 (2017) 064 [arXiv:1610.09178] [INSPIRE].
P. Agarwal, K. Maruyoshi and J. Song, A “Lagrangian” for the E7 superconformal theory, JHEP 05 (2018) 193 [arXiv:1802.05268] [INSPIRE].
H.-C. Kim, S.S. Razamat, C. Vafa and G. Zafrir, E-String Theory on Riemann Surfaces, Fortsch. Phys. 66 (2018) 1700074 [arXiv:1709.02496] [INSPIRE].
S.S. Razamat and G. Zafrir, N = 1 conformal dualities, JHEP 09 (2019) 046 [arXiv:1906.05088] [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 and N. Seiberg, S-duality in N = 2 supersymmetric gauge theories, JHEP 12 (2007) 088 [arXiv:0711.0054] [INSPIRE].
H.-C. Kim, S.S. Razamat, C. Vafa and G. Zafrir, D-type Conformal Matter and SU/USp Quivers, JHEP 06 (2018) 058 [arXiv:1802.00620] [INSPIRE].
O. Aharony and Y. Tachikawa, A Holographic computation of the central charges of d = 4, N = 2 SCFTs, JHEP 01 (2008) 037 [arXiv:0711.4532] [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].
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 Superconformal Index of the E6 SCFT, JHEP 08 (2010) 107 [arXiv:1003.4244] [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].
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].
D. Gaiotto and S.S. Razamat, Exceptional Indices, JHEP 05 (2012) 145 [arXiv:1203.5517] [INSPIRE].
D. Gaiotto, L. Rastelli and S.S. Razamat, Bootstrapping the superconformal index with surface defects, JHEP 01 (2013) 022 [arXiv:1207.3577] [INSPIRE].
F. Benini, Y. Tachikawa and B. Wecht, Sicilian gauge theories and N = 1 dualities, JHEP 01 (2010) 088 [arXiv:0909.1327] [INSPIRE].
O. Bergman and G. Zafrir, Lifting 4d dualities to 5d, JHEP 04 (2015) 141 [arXiv:1410.2806] [INSPIRE].
G. Ferlito, A. Hanany, N. Mekareeya and G. Zafrir, 3d Coulomb branch and 5d Higgs branch at infinite coupling, JHEP 07 (2018) 061 [arXiv:1712.06604] [INSPIRE].
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Zafrir, G. An \( \mathcal{N} \) = 1 Lagrangian for the rank 1 E6 superconformal theory. J. High Energ. Phys. 2020, 98 (2020). https://doi.org/10.1007/JHEP12(2020)098
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DOI: https://doi.org/10.1007/JHEP12(2020)098