Abstract
We generalize S-duality to \( \mathcal{N}=2 \) superconformal field theories (SCFTs) with Coulomb branch operators of non-integer scaling dimension. As simple examples, we find minimal generalizations of the S-dualities discovered in SU(2) gauge theory with four fundamental flavors by Seiberg and Witten and in SU(3) gauge theory with six fundamental flavors by Argyres and Seiberg. Our constructions start by weakly gauging diagonal SU(2) and SU(3) flavor symmetry subgroups of two copies of a particular rank-one Argyres-Douglas theory (along with sufficient numbers of hypermultiplets to guarantee conformality of the gauging). As we explore the resulting conformal manifold of the SU(2) SCFT, we find an action of S-duality on the parameters of the theory that is reminiscent of Spin(8) triality. On the other hand, as we explore the conformal manifold of the SU(3) theory, we find that an exotic rank-two SCFT emerges in a dual SU(2) description.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
V. Asnin, On metric geometry of conformal moduli spaces of four-dimensional superconformal theories, JHEP 09 (2010) 012 [arXiv:0912.2529] [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].
C. Montonen and D.I. Olive, Magnetic monopoles as gauge particles?, Phys. Lett. B 72 (1977) 117 [INSPIRE].
P. Goddard, J. Nuyts and D.I. Olive, Gauge theories and magnetic charge, Nucl. Phys. B 125 (1977) 1 [INSPIRE].
E. Witten and D.I. Olive, Supersymmetry algebras that include topological charges, Phys. Lett. B 78 (1978) 97 [INSPIRE].
H. Osborn, Topological charges for N = 4 supersymmetric gauge theories and monopoles of spin 1, Phys. Lett. B 83 (1979) 321 [INSPIRE].
P.C. Argyres and N. Seiberg, S-duality in N = 2 supersymmetric gauge theories, JHEP 12 (2007) 088 [arXiv:0711.0054] [INSPIRE].
J.A. Minahan and D. Nemeschansky, An N = 2 superconformal fixed point with E 6 global symmetry, Nucl. Phys. B 482 (1996) 142 [hep-th/9608047] [INSPIRE].
D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [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].
O. Chacaltana and J. Distler, Tinkertoys for Gaiotto duality, JHEP 11 (2010) 099 [arXiv:1008.5203] [INSPIRE].
P.C. Argyres and M.R. Douglas, New phenomena in SU(3) supersymmetric gauge theory, Nucl. Phys. B 448 (1995) 93 [hep-th/9505062] [INSPIRE].
P.C. Argyres, M.R. 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].
D. Xie and P. Zhao, Central charges and RG flow of strongly-coupled N = 2 theory, JHEP 03 (2013) 006 [arXiv:1301.0210] [INSPIRE].
S. Cecotti, A. Neitzke and C. Vafa, R-twisting and 4d/2d correspondences, arXiv:1006.3435 [INSPIRE].
K. Kodaira, On compact analytic surfaces II, Ann. Math. 77 (1963) 563.
S. Giacomelli, Confinement and duality in supersymmetric gauge theories, arXiv:1309.5299 [INSPIRE].
D. Xie, General Argyres-Douglas theory, JHEP 01 (2013) 100 [arXiv:1204.2270] [INSPIRE].
E. Witten, An SU(2) anomaly, Phys. Lett. B 117 (1982) 324 [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].
M. Buican, Minimal distances between SCFTs, JHEP 01 (2014) 155 [arXiv:1311.1276] [INSPIRE].
F.A. Dolan and H. Osborn, On short and semi-short representations for four-dimensional superconformal symmetry, Annals Phys. 307 (2003) 41 [hep-th/0209056] [INSPIRE].
K. Papadodimas, Topological anti-topological fusion in four-dimensional superconformal field theories, JHEP 08 (2010) 118 [arXiv:0910.4963] [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].
S. Cecotti and C. Vafa, Classification of complete N = 2 supersymmetric theories in 4 dimensions, Surveys in differential geometry, vol 18 (2013) [arXiv:1103.5832] [INSPIRE].
D. Gaiotto, G.W. Moore and A. Neitzke, Spectral networks and snakes, Annales Henri Poincaré 15 (2014) 61 [arXiv:1209.0866] [INSPIRE].
D. Gaiotto, G.W. Moore and A. Neitzke, Wall-crossing, Hitchin systems and the WKB approximation, arXiv:0907.3987 [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].
D. Nanopoulos and D. Xie, More three dimensional mirror pairs, JHEP 05 (2011) 071 [arXiv:1011.1911] [INSPIRE].
P. Boalch, Irregular connections and Kac-Moody root systems, arXiv:0806.1050.
P. Boalch, Hyperkähler manifolds and nonabelian Hodge theory of (irregular) curves, arXiv:1203.6607.
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].
A. Zhiboedov, On conformal field theories with extremal a/c values, JHEP 04 (2014) 038 [arXiv:1304.6075] [INSPIRE].
J. de Boer, K. Hori, H. Ooguri, Y. Oz and Z. Yin, Mirror symmetry in three-dimensional theories, \( \mathrm{S}\mathrm{L}\left(2,\mathrm{\mathbb{Z}}\right) \) and D-brane moduli spaces, Nucl. Phys. B 493 (1997) 148 [hep-th/9612131] [INSPIRE].
P.C. Argyres, M.R. Plesser and A.D. Shapere, The coulomb phase of N = 2 supersymmetric QCD, Phys. Rev. Lett. 75 (1995) 1699 [hep-th/9505100] [INSPIRE].
E. Witten, Solutions of four-dimensional field theories via M-theory, Nucl. Phys. B 500 (1997) 3 [hep-th/9703166] [INSPIRE].
S. Cremonesi, G. Ferlito, A. Hanany and N. Mekareeya, Coulomb branch and the moduli space of instantons, JHEP 12 (2014) 103 [arXiv:1408.6835] [INSPIRE].
M. Buican and T. Nishinaka, Compact conformal manifolds, JHEP 01 (2015) 112 [arXiv:1410.3006] [INSPIRE].
S. Cecotti, M. Del Zotto and S. Giacomelli, More on the \( \mathcal{N}=2 \) uperconformal systems of type D p (G), JHEP 04 (2013) 153 [arXiv:1303.3149] [INSPIRE].
I. Yaakov, Redeeming bad theories, JHEP 11 (2013) 189 [arXiv:1303.2769] [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: 1411.6026
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
Buican, M., Giacomelli, S., Nishinaka, T. et al. Argyres-Douglas theories and S-duality. J. High Energ. Phys. 2015, 185 (2015). https://doi.org/10.1007/JHEP02(2015)185
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2015)185