Abstract
We discuss two infinite classes of 4d supersymmetric theories, T (m) N and \( {\mathcal{U}}_N^{(m)} \), labelled by an arbitrary non-negative integer, m. The T (m) N theory arises from the 6d, A N − 1 type \( \mathcal{N}=\left(2,0\right) \) theory reduced on a 3-punctured sphere, with normal bundle given by line bundles of degree (m + 1, −m); the m = 0 case is the \( \mathcal{N}=2 \) supersymmetric T N theory. The novelty is the negative-degree line bundle. The \( {\mathcal{U}}_N^{(m)} \) theories likewise arise from the 6d \( \mathcal{N}=\left(2,0\right) \) theory on a 4-punctured sphere, and can be regarded as gluing together two (partially Higgsed) T (m) N theories. The T (m) N and \( {\mathcal{U}}_N^{(m)} \) theories can be represented, in various duality frames, as quiver gauge theories, built from T N components via gauging and nilpotent Higgsing. We analyze the RG flow of the \( {\mathcal{U}}_N^{(m)} \) theories, and find that, for all integer m > 0, they end up at the same IR SCFT as SU(N) SQCD with 2N flavors and quartic superpotential. The \( {\mathcal{U}}_N^{(m)} \) theories can thus be regarded as an infinite set of UV completions, dual to SQCD with N f = 2N c . The \( {\mathcal{U}}_N^{(m)} \) duals have different duality frame quiver representations, with 2m + 1 gauge nodes.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N. Seiberg, Electric-magnetic duality in supersymmetric non-Abelian gauge theories, Nucl. Phys. B 435 (1995) 129 [hep-th/9411149] [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].
P.C. Argyres, M.R. Plesser and N. Seiberg, The moduli space of vacua of N = 2 SUSY QCD and duality in N = 1 SUSY QCD, Nucl. Phys. B 471 (1996) 159 [hep-th/9603042] [INSPIRE].
A. Gadde, K. Maruyoshi, Y. Tachikawa and W. Yan, New N = 1 dualities, JHEP 06 (2013) 056 [arXiv:1303.0836] [INSPIRE].
D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].
Y. Tachikawa, A review of the T N theory and its cousins, Prog. Theor. Exp. Phys. 2015 (2015) 11B102 [arXiv:1504.01481] [INSPIRE].
P. Agarwal, I. Bah, K. Maruyoshi and J. Song, Quiver tails and N = 1 SCFTs from M5-branes, JHEP 03 (2015) 049 [arXiv:1409.1908] [INSPIRE].
K.A. Intriligator and P. Pouliot, Exact superpotentials, quantum vacua and duality in supersymmetric SP(N c ) gauge theories, Phys. Lett. B 353 (1995) 471 [hep-th/9505006] [INSPIRE].
C. Csáki, M. Schmaltz, W. Skiba and J. Terning, Selfdual N = 1 SUSY gauge theories, Phys. Rev. D 56 (1997) 1228 [hep-th/9701191] [INSPIRE].
N. Seiberg, Exact results on the space of vacua of four-dimensional SUSY gauge theories, Phys. Rev. D 49 (1994) 6857 [hep-th/9402044] [INSPIRE].
K.A. Intriligator and N. Seiberg, Lectures on supersymmetric gauge theories and electric-magnetic duality, Nucl. Phys. Proc. Suppl. 45BC (1996) 1 [hep-th/9509066] [INSPIRE].
K. Maruyoshi, Y. Tachikawa, W. Yan and K. Yonekura, N = 1 dynamics with T N theory, JHEP 10 (2013) 010 [arXiv:1305.5250] [INSPIRE].
K.A. Intriligator and B. Wecht, The exact superconformal R symmetry maximizes a, Nucl. Phys. B 667 (2003) 183 [hep-th/0304128] [INSPIRE].
C. Romelsberger, Counting chiral primaries in N = 1, D = 4 superconformal field theories, Nucl. Phys. B 747 (2006) 329 [hep-th/0510060] [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].
D. Gaiotto, G.W. Moore and A. Neitzke, Wall-crossing, Hitchin systems and the WKB approximation, arXiv:0907.3987 [INSPIRE].
F. Benini, Y. Tachikawa and B. Wecht, Sicilian gauge theories and N = 1 dualities, JHEP 01 (2010) 088 [arXiv:0909.1327] [INSPIRE].
I. Bah, C. Beem, N. Bobev and B. Wecht, AdS/CFT dual pairs from M 5-branes on Riemann surfaces, Phys. Rev. D 85 (2012) 121901 [arXiv:1112.5487] [INSPIRE].
I. Bah, C. Beem, N. Bobev and B. Wecht, Four-dimensional SCFTs from M5-branes, JHEP 06 (2012) 005 [arXiv:1203.0303] [INSPIRE].
D. Xie, M5 brane and four dimensional N = 1 theories I, JHEP 04 (2014) 154 [arXiv:1307.5877] [INSPIRE].
K. Maruyoshi, M. Taki, S. Terashima and F. Yagi, New Seiberg dualities from N = 2 dualities, JHEP 09 (2009) 086 [arXiv:0907.2625] [INSPIRE].
I. Bah and B. Wecht, New N = 1 superconformal field theories in four dimensions, JHEP 07 (2013) 107 [arXiv:1111.3402] [INSPIRE].
C. Beem and A. Gadde, The N = 1 superconformal index for class S fixed points, JHEP 04 (2014) 036 [arXiv:1212.1467] [INSPIRE].
I. Bah and N. Bobev, Linear quivers and N = 1 SCFTs from M5-branes, JHEP 08 (2014) 121 [arXiv:1307.7104] [INSPIRE].
P. Agarwal and J. Song, New N = 1 dualities from M5-branes and outer-automorphism twists, JHEP 03 (2014) 133 [arXiv:1311.2945] [INSPIRE].
J. McGrane and B. Wecht, Theories of class S and new N = 1 SCFTs, JHEP 06 (2015) 047 [arXiv:1409.7668] [INSPIRE].
I. Bah, Quarter-BPS AdS 5 solutions in M-theory with a T 2 bundle over a Riemann surface, JHEP 08 (2013) 137 [arXiv:1304.4954] [INSPIRE].
I. Bah, M. Gabella and N. Halmagyi, Punctures from probe M5-branes and N = 1 superconformal field theories, JHEP 07 (2014) 131 [arXiv:1312.6687] [INSPIRE].
I. Bah, AdS 5 solutions from M5-branes on Riemann surface and D6-branes sources, arXiv:1501.06072 [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 and K. Yonekura, Generalized Hitchin system, spectral curve and N = 1 dynamics, JHEP 01 (2014) 001 [arXiv:1310.0467] [INSPIRE].
K. Yonekura, Supersymmetric gauge theory, (2, 0) theory and twisted 5d super-Yang-Mills, JHEP 01 (2014) 142 [arXiv:1310.7943] [INSPIRE].
D. Xie, N = 1 curve, arXiv:1409.8306 [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].
O. Chacaltana and J. Distler, Tinkertoys for Gaiotto duality, JHEP 11 (2010) 099 [arXiv:1008.5203] [INSPIRE].
O. Chacaltana, J. Distler and Y. Tachikawa, Nilpotent orbits and codimension-two defects of 6d N = (2, 0) theories, Int. J. Mod. Phys. A 28 (2013) 1340006 [arXiv:1203.2930] [INSPIRE].
N. Seiberg and E. Witten, Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD, Nucl. Phys. B 431 (1994) 484 [hep-th/9408099] [INSPIRE].
V.P. Spiridonov and G.S. Vartanov, Superconformal indices for N = 1 theories with multiple duals, Nucl. Phys. B 824 (2010) 192 [arXiv:0811.1909] [INSPIRE].
T. Dimofte and D. Gaiotto, An E 7 surprise, JHEP 10 (2012) 129 [arXiv:1209.1404] [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].
D. Anselmi, D.Z. Freedman, M.T. Grisaru and A.A. Johansen, Nonperturbative formulas for central functions of supersymmetric gauge theories, Nucl. Phys. B 526 (1998) 543 [hep-th/9708042] [INSPIRE].
D. Anselmi, J. Erlich, D.Z. Freedman and A.A. Johansen, Positivity constraints on anomalies in supersymmetric gauge theories, Phys. Rev. D 57 (1998) 7570 [hep-th/9711035] [INSPIRE].
D. Gaiotto and J. Maldacena, The gravity duals of N = 2 superconformal field theories, JHEP 10 (2012) 189 [arXiv:0904.4466] [INSPIRE].
A. Gadde, E. Pomoni, L. Rastelli and S.S. Razamat, S-duality and 2d topological QFT, JHEP 03 (2010) 032 [arXiv:0910.2225] [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, L. Rastelli and S.S. Razamat, Bootstrapping the superconformal index with surface defects, JHEP 01 (2013) 022 [arXiv:1207.3577] [INSPIRE].
L. Rastelli and S.S. Razamat, The superconformal index of theories of class S, arXiv:1412.7131 [INSPIRE].
N. Mekareeya, J. Song and Y. Tachikawa, 2d TQFT structure of the superconformal indices with outer-automorphism twists, JHEP 03 (2013) 171 [arXiv:1212.0545] [INSPIRE].
H. Hayashi, Y. Tachikawa and K. Yonekura, Mass-deformed T N as a linear quiver, JHEP 02 (2015) 089 [arXiv:1410.6868] [INSPIRE].
S. Giacomelli, Four dimensional superconformal theories from M5 branes, JHEP 01 (2015) 044 [arXiv:1409.3077] [INSPIRE].
Y. Tachikawa, Six-dimensional D N theory and four-dimensional SO-USp quivers, JHEP 07 (2009) 067 [arXiv:0905.4074] [INSPIRE].
Y. Tachikawa, N = 2 S-duality via outer-automorphism twists, J. Phys. A 44 (2011) 182001 [arXiv:1009.0339] [INSPIRE].
O. Chacaltana and J. Distler, Tinkertoys for the D N series, JHEP 02 (2013) 110 [arXiv:1106.5410] [INSPIRE].
O. Chacaltana, J. Distler and Y. Tachikawa, Gaiotto duality for the twisted A 2N − 1 series, JHEP 05 (2015) 075 [arXiv:1212.3952] [INSPIRE].
O. Chacaltana, J. Distler and A. Trimm, Tinkertoys for the twisted D-series, JHEP 04 (2015) 173 [arXiv:1309.2299] [INSPIRE].
O. Chacaltana, J. Distler and A. Trimm, Tinkertoys for the E 6 theory, JHEP 09 (2015) 007 [arXiv:1403.4604] [INSPIRE].
O. Chacaltana, J. Distler and A. Trimm, Tinkertoys for the twisted E 6 theory, arXiv:1501.00357 [INSPIRE].
D. Gaiotto and S.S. Razamat, N = 1 theories of class S k , JHEP 07 (2015) 073 [arXiv:1503.05159] [INSPIRE].
S. Franco, H. Hayashi and A. Uranga, Charting class S k territory, Phys. Rev. D 92 (2015) 045004 [arXiv:1504.05988] [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: 1505.00255
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
Agarwal, P., Intriligator, K. & Song, J. Infinitely many \( \mathcal{N}=1 \) dualities from m + 1 − m = 1. J. High Energ. Phys. 2015, 35 (2015). https://doi.org/10.1007/JHEP10(2015)035
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2015)035