Abstract
We introduce a class of four dimensional field theories constructed by quotienting ordinary \( \mathcal{N}=4 \) U(N ) SYM by particular combinations of R-symmetry and SL(2, ℤ) automorphisms. These theories appear naturally on the worldvolume of D3 branes probing terminal singularities in F-theory, where they can be thought of as non-perturbative generalizations of the O3 plane. We focus on cases preserving only 12 supercharges, where the quotient gives rise to theories with coupling fixed at a value of order one. These constructions possess an unconventional large N limit described by a non-trivial F-theory fibration with base AdS 5 × (S 5/ℤ k ). Upon reduction on a circle the \( \mathcal{N}=3 \) theories flow to well-known \( \mathcal{N}=6 \) ABJM theories.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C. Vafa, Evidence for F-theory, Nucl. Phys. B 469 (1996) 403 [hep-th/9602022] [INSPIRE].
R. Donagi and M. Wijnholt, Model Building with F-theory, Adv. Theor. Math. Phys. 15 (2011) 1237 [arXiv:0802.2969] [INSPIRE].
C. Beasley, J.J. Heckman and C. Vafa, GUTs and Exceptional Branes in F-theory — I, JHEP 01 (2009) 058 [arXiv:0802.3391] [INSPIRE].
H. Hayashi, R. Tatar, Y. Toda, T. Watari and M. Yamazaki, New Aspects of Heterotic-F Theory Duality, Nucl. Phys. B 806 (2009) 224 [arXiv:0805.1057] [INSPIRE].
C. Beasley, J.J. Heckman and C. Vafa, GUTs and Exceptional Branes in F-theory — II: Experimental Predictions, JHEP 01 (2009) 059 [arXiv:0806.0102] [INSPIRE].
E. Witten, Phase transitions in M-theory and F-theory, Nucl. Phys. B 471 (1996) 195 [hep-th/9603150] [INSPIRE].
O. Aharony, O. Bergman, D.L. Jafferis and J.M. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
O. Aharony, O. Bergman and D.L. Jafferis, Fractional M2-branes, JHEP 11 (2008) 043 [arXiv:0807.4924] [INSPIRE].
S. Weinberg, The quantum theory of fields. Volume 3: Supersymmetry, Cambridge University Press (2013).
A.E. Lawrence, N. Nekrasov and C. Vafa, On conformal field theories in four-dimensions, Nucl. Phys. B 533 (1998) 199 [hep-th/9803015] [INSPIRE].
O. Aharony and M. Evtikhiev, On four dimensional N = 3 superconformal theories, arXiv:1512.03524 [INSPIRE].
J. Polchinski, String theory. Volume 2: Superstring theory and beyond, Cambridge University Press (2007).
D.R. Morrison and G. Stevens, Terminal quotient singularities in dimensions three and four, Proc. Am. Math. Soc. 90 (1984) 15.
R. Anno, Four-Dimensional Terminal Gorenstein Quotient Singularities, Math. Notes 73 (2003) 769.
A. Kapustin and E. Witten, Electric-Magnetic Duality And The Geometric Langlands Program, Commun. Num. Theor. Phys. 1 (2007) 1 [hep-th/0604151] [INSPIRE].
E. Witten, Baryons and branes in anti-de Sitter space, JHEP 07 (1998) 006 [hep-th/9805112] [INSPIRE].
Y. Hyakutake, Y. Imamura and S. Sugimoto, Orientifold planes, type-I Wilson lines and non-BPS D-branes, JHEP 08 (2000) 043 [hep-th/0007012] [INSPIRE].
A. Hanany and B. Kol, On orientifolds, discrete torsion, branes and M-theory, JHEP 06 (2000) 013 [hep-th/0003025] [INSPIRE].
K. Dasgupta and S. Mukhi, F theory at constant coupling, Phys. Lett. B 385 (1996) 125 [hep-th/9606044] [INSPIRE].
S. Dulat and K. Wendland, Crystallographic orbifolds: Towards a classification of unitary conformal field theories with central charge c = 2, JHEP 06 (2000) 012 [hep-th/0002227] [INSPIRE].
L. Nilse, Classification of 1D and 2D orbifolds, hep-ph/0601015 [INSPIRE].
O. Bergman and S. Hirano, Anomalous radius shift in AdS 4 /CF T 3, JHEP 07 (2009) 016 [arXiv:0902.1743] [INSPIRE].
S. Sethi, A Relation between N = 8 gauge theories in three-dimensions, JHEP 11 (1998) 003 [hep-th/9809162] [INSPIRE].
M. Bianchi, A. Collinucci and L. Martucci, Magnetized E3-brane instantons in F-theory, JHEP 12 (2011) 045 [arXiv:1107.3732] [INSPIRE].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].
A. Font and J.A. Lopez, Strings on eight-orbifolds, Nucl. Phys. B 703 (2004) 177 [hep-th/0405151] [INSPIRE].
D. Gang, E. Koh, K. Lee and J. Park, ABCD of 3d \( \mathcal{N}=8 \) and 4 Superconformal Field Theories, arXiv:1108.3647 [INSPIRE].
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].
A. Galperin, E. Ivanov, S. Kalitsyn, V. Ogievetsky and E. Sokatchev, N = 3 supersymmetric gauge theory, Phys. Lett. B 151 (1985) 215 [INSPIRE].
F. Delduc and J. McCabe, The Quantization of N = 3 Super Yang-Mills Off-shell in Harmonic Superspace, Class. Quant. Grav. 6 (1989) 233 [INSPIRE].
E.A. Ivanov and B.M. Zupnik, N = 3 supersymmetric Born-Infeld theory, Nucl. Phys. B 618 (2001) 3 [hep-th/0110074] [INSPIRE].
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].
A.S. Galperin, E.A. Ivanov, V.I. Ogievetsky and E.S. Sokatchev, Harmonic Superspace, Cambridge University Press (2007).
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].
A. Collinucci and R. Savelli, F-theory on singular spaces, JHEP 09 (2015) 100 [arXiv:1410.4867] [INSPIRE].
A. Kapustin, Lectures on Electric-Magnetic Duality and the Geometric Langlands Program, http://www.ctqm.au.dk/research/MCS/LectureNotesKapustin.pdf (2008).
J.E. Kiskis, Disconnected Gauge Groups and the Global Violation of Charge Conservation, Phys. Rev. D 17 (1978) 3196 [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: 1512.06434
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
García-Etxebarria, I., Regalado, D. \( \mathcal{N}=3 \) four dimensional field theories. J. High Energ. Phys. 2016, 83 (2016). https://doi.org/10.1007/JHEP03(2016)083
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2016)083