On four dimensional N = 3 superconformal theories
- 112 Downloads
- 9 Citations
Abstract
In this note we study four dimensional theories with N = 3 superconformal symmetry, that do not also have N = 4 supersymmetry. No examples of such theories are known, but their existence is also not ruled out. We analyze several properties that such theories must have. We show that their conformal anomalies obey a = c. Using the N = 3 superconformal algebra, we show that they do not have any exactly marginal deformations preserving N = 3 supersymmetry, or global symmetries (except for their R-symmetries). Finally, we analyze the possible dimensions of chiral operators labeling their moduli space.
Keywords
Extended Supersymmetry Supersymmetric gauge theoryNotes
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.
References
- [1]A. Giveon and D. Kutasov, Brane dynamics and gauge theory, Rev. Mod. Phys. 71 (1999) 983 [hep-th/9802067] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
- [2]D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
- [3]S. Ferrara, M. Porrati and A. Zaffaroni, N = 6 supergravity on AdS 5 and the SU(2, 2/3) superconformal correspondence, Lett. Math. Phys. 47 (1999) 255 [hep-th/9810063] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
- [4]S.W. Beck, J.B. Gutowski and G. Papadopoulos, AdS5 Backgrounds with 24 Supersymmetries, arXiv:1601.06645 [INSPIRE].
- [5]I. García-Etxebarria and D. Regalado, \( \mathcal{N}=3 \) four dimensional field theories, JHEP 03 (2016) 083 [arXiv:1512.06434] [INSPIRE].
- [6]T. Nishinaka and Y. Tachikawa, On 4d rank-one N = 3 superconformal field theories, arXiv:1602.01503 [INSPIRE].
- [7]O. Aharony and Y. Tachikawa, S-folds and 4d N = 3 superconformal field theories, arXiv:1602.08638 [INSPIRE].
- [8]C. Beem, L. Rastelli and B.C. van Rees, The \( \mathcal{N}=4 \) Superconformal Bootstrap, Phys. Rev. Lett. 111 (2013) 071601 [arXiv:1304.1803] [INSPIRE].ADSCrossRefGoogle Scholar
- [9]C. Beem, M. Lemos, P. Liendo, L. Rastelli and B.C. van Rees, The \( \mathcal{N}=2 \) superconformal bootstrap, JHEP 03 (2016) 183 [arXiv:1412.7541] [INSPIRE].CrossRefGoogle Scholar
- [10]D.M. Hofman and J. Maldacena, Conformal collider physics: energy and charge correlations, JHEP 05 (2008) 012 [arXiv:0803.1467] [INSPIRE].ADSCrossRefGoogle Scholar
- [11]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].ADSMathSciNetCrossRefMATHGoogle Scholar
- [12]P.C. Argyres, M. Crescimanno, A.D. Shapere and J.R. Wittig, Classification of N = 2 superconformal field theories with two-dimensional Coulomb branches, hep-th/0504070 [INSPIRE].
- [13]P.C. Argyres and J.R. Wittig, Classification of N = 2 superconformal field theories with two-dimensional Coulomb branches. II, hep-th/0510226 [INSPIRE].
- [14]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].ADSMathSciNetCrossRefMATHGoogle Scholar
- [15]P.C. Argyres and J. Wittig, Mass deformations of four-dimensional, rank 1, N = 2 superconformal field theories, J. Phys. Conf. Ser. 462 (2013) 012001 [arXiv:1007.5026] [INSPIRE].CrossRefGoogle Scholar
- [16]P. Argyres, M. Lotito, Y. Lü and M. Martone, Geometric constraints on the space of N = 2 SCFTs I: physical constraints on relevant deformations, arXiv:1505.04814 [INSPIRE].
- [17]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].ADSMathSciNetCrossRefMATHGoogle Scholar
- [18]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].ADSMathSciNetCrossRefMATHGoogle Scholar
- [19]S.M. Kuzenko and S. Theisen, Correlation functions of conserved currents in N = 2 superconformal theory, Class. Quant. Grav. 17 (2000) 665 [hep-th/9907107] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
- [20]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].ADSMathSciNetCrossRefMATHGoogle Scholar
- [21]Y. Tachikawa, N = 2 supersymmetric dynamics for pedestrians, Lect. Notes Phys. 890 (2013) 2014 [arXiv:1312.2684] [INSPIRE].MathSciNetGoogle Scholar
- [22]A. Galperin, E. Ivanov, S. Kalitsyn, V. Ogievetsky and E. Sokatchev, N = 3 supersymmetric gauge theory, Phys. Lett. B 151 (1985) 215 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
- [23]A. Galperin, E. Ivanov, S. Kalitsyn, V. Ogievetsky and E. Sokatchev, Unconstrained Off-Shell N =3 Supersymmetric Yang-Mills Theory, Class. Quant. Grav. 2(1985) 155[INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
- [24]I.L. Buchbinder, E.A. Ivanov, I.B. Samsonov and B.M. Zupnik, Scale invariant low-energy effective action in N = 3 SYM theory, Nucl. Phys. B 689 (2004) 91 [hep-th/0403053] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
- [25]I.L. Buchbinder, E.A. Ivanov, I.B. Samsonov and B.M. Zupnik, Superconformal N = 3 SYM Low-Energy Effective Action, JHEP 01 (2012) 001 [arXiv:1111.4145] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
- [26]C. Cordova, T.T. Dumitrescu and K. Intriligator, Deformations of Superconformal Theories, arXiv:1602.01217 [INSPIRE].
- [27]V.K. Dobrev and V.B. Petkova, All Positive Energy Unitary Irreducible Representations of Extended Conformal Supersymmetry, Phys. Lett. B 162 (1985) 127 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
- [28]S. Minwalla, Restrictions imposed by superconformal invariance on quantum field theories, Adv. Theor. Math. Phys. 2 (1998) 781 [hep-th/9712074] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar