Abstract
Four dimensional \( \mathcal{N} \) = 1 theories are engineered by compactifying six dimensional (2, 0) theory on a Riemann surface with regular punctures. A generalized Hitchin’s equation involving two Higgs fields is proposed as the BPS equation for \( \mathcal{N} \) = 1 compactification. The puncture is interpreted as the singular boundary condition of this equation, and regular puncture is shown to be labeled by a nilpotent commuting pair. In this paper, we focus on a subset of regular puncture which is described by rotating branes representing \( \mathcal{N} \) =2 puncture. As an application, we show that Seiberg duality of SU(N) SQCD with N f = 2N and certain superpotential term is realized as different degeneration limits of the same punctured Riemann surface, and find four more dual theories.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Giveon and D. Kutasov, Brane dynamics and gauge theory, Rev. Mod. Phys. 71 (1999) 983 [hep-th/9802067] [INSPIRE].
E. Witten, Solutions of four-dimensional field theories via M-theory, Nucl. Phys. B 500 (1997) 3 [hep-th/9703166] [INSPIRE].
E. Witten, Branes and the dynamics of QCD, Nucl. Phys. B 507 (1997) 658 [hep-th/9706109] [INSPIRE].
K. Hori, H. Ooguri and Y. Oz, Strong coupling dynamics of four-dimensional N = 1 gauge theories from M-theory five-brane, Adv. Theor. Math. Phys. 1 (1998) 1 [hep-th/9706082] [INSPIRE].
P.C. Argyres and N. Seiberg, S-duality in N = 2 supersymmetric gauge theories, JHEP 12 (2007) 088 [arXiv:0711.0054] [INSPIRE].
D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].
J.M. Maldacena and C. Núñez, Supergravity description of field theories on curved manifolds and a no go theorem, Int. J. Mod. Phys. A 16 (2001) 822 [hep-th/0007018] [INSPIRE].
J.M. Maldacena and C. Núñez, Towards the large-N limit of pure N = 1 super Yang-Mills, Phys. Rev. Lett. 86 (2001) 588 [hep-th/0008001] [INSPIRE].
J.P. Gauntlett, Branes, calibrations and supergravity, hep-th/0305074 [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, 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].
O. Chacaltana, J. Distler and Y. Tachikawa, Gaiotto Duality for the Twisted A2N−1 Series, arXiv:1212.3952 [INSPIRE].
D. Gaiotto, G.W. Moore and A. Neitzke, Wall-crossing, Hitchin Systems and the WKB Approximation, arXiv:0907.3987 [INSPIRE].
D. Nanopoulos and D. Xie, Hitchin Equation, Singularity and N = 2 Superconformal Field Theories, JHEP 03 (2010) 043 [arXiv:0911.1990] [INSPIRE].
D. Nanopoulos and D. Xie, N = 2 Generalized Superconformal Quiver Gauge Theory, JHEP 09 (2012) 127 [arXiv:1006.3486] [INSPIRE].
O. Chacaltana and J. Distler, Tinkertoys for Gaiotto Duality, JHEP 11 (2010) 099 [arXiv:1008.5203] [INSPIRE].
D. Xie, General Argyres-Douglas Theory, JHEP 01 (2013) 100 [arXiv:1204.2270] [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].
F. Benini, Y. Tachikawa and B. Wecht, Sicilian gauge theories and N = 1 dualities, JHEP 01 (2010) 088 [arXiv:0909.1327] [INSPIRE].
I. Bah and B. Wecht, New N = 1 Superconformal Field Theories In Four Dimensions, JHEP 07 (2013) 107 [arXiv:1111.3402] [INSPIRE].
I. Bah, C. Beem, N. Bobev and B. Wecht, AdS/CFT Dual Pairs from M5-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].
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, K. Maruyoshi, Y. Tachikawa and W. Yan, New N = 1 Dualities, JHEP 06 (2013) 056 [arXiv:1303.0836] [INSPIRE].
V. Ginzburg, Principal nilpotent pairs in a semisimple lie algebra 1, Inv. Math. 140 (2000) 511.
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. Hashimoto, P. Ouyang and M. Yamazaki, Work in progress.
S. Elitzur, A. Giveon and D. Kutasov, Branes and N = 1 duality in string theory, Phys. Lett. B 400 (1997) 269 [hep-th/9702014] [INSPIRE].
S. Elitzur, A. Giveon, D. Kutasov, E. Rabinovici and A. Schwimmer, Brane dynamics and N =1 supersymmetric gauge theory, Nucl. Phys. B 505 (1997) 202 [hep-th/9704104] [INSPIRE].
N. Seiberg, Electric-magnetic duality in supersymmetric nonAbelian 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].
M. Bershadsky, A. Johansen, V. Sadov and C. Vafa, Topological reduction of 4 − D SYM to 2 − D σ-models, Nucl. Phys. B 448 (1995) 166 [hep-th/9501096] [INSPIRE].
M.T. Anderson, C. Beem, N. Bobev and L. Rastelli, Holographic Uniformization, Commun. Math. Phys. 318 (2013) 429 [arXiv:1109.3724] [INSPIRE].
A. Kapustin and E. Witten, Electric-Magnetic Duality And The Geometric Langlands Program, Commun. Num. Theor. Phys. 1 (2007) 1 [hep-th/0604151] [INSPIRE].
N. Hitchin, The self-duality equation on a riemann surface, Proc. London Math. Soc. 55 (1987) 59.
S. Gukov and E. Witten, Gauge Theory, Ramification, And The Geometric Langlands Program, hep-th/0612073 [INSPIRE].
N. Hitchin, Stable bundles and integrable system, Duke Math. J. 54 (1987) 91.
D. Gaiotto and E. Witten, Supersymmetric Boundary Conditions in N = 4 Super Yang-Mills Theory, J. Statist. Phys. 135 (2009) 789 [arXiv:0804.2902] [INSPIRE].
F. Benini, Y. Tachikawa and D. Xie, Mirrors of 3d Sicilian theories, JHEP 09 (2010) 063 [arXiv:1007.0992] [INSPIRE].
E. Corrigan, C. Devchand, D.B. Fairlie and J. Nuyts, First Order Equations for Gauge Fields in Spaces of Dimension Greater Than Four, Nucl. Phys. B 214 (1983) 452 [INSPIRE].
D.-s. Bak, K.-M. Lee and J.-H. Park, BPS equations in six-dimensions and eight-dimensions, Phys. Rev. D 66 (2002) 025021 [hep-th/0204221] [INSPIRE].
M.F. Atiyah and R. Bott, The Yang-Mills equations over riemann surfaces, Phil. Transact. Roy. Soc. London Series A (1983) 523.
N. Nitsure, Moduli space of semistable pairs on a curve, Proc. London Math. Soc. 3 (1991) 275.
O. Aharony and A. Hanany, Branes, superpotentials and superconformal fixed points, Nucl. Phys. B 504 (1997) 239 [hep-th/9704170] [INSPIRE].
O. Chacaltana and J. Distler, Tinkertoys for the D N series, JHEP 02 (2013) 110 [arXiv:1106.5410] [INSPIRE].
I.R. Klebanov and E. Witten, Superconformal field theory on three-branes at a Calabi-Yau singularity, Nucl. Phys. B 536 (1998) 199 [hep-th/9807080] [INSPIRE].
D. Xie, M5 brane and four dimensional N = 1 theory II: general punctures, work in progress.
T. Eguchi and Y. Sugawara, Branches of N = 1 vacua and Argyres-Douglas points, JHEP 05 (2003) 063 [hep-th/0305050] [INSPIRE].
O. Aharony, S.S. Razamat, N. Seiberg and B. Willett, 3d dualities from 4d dualities, JHEP 07 (2013) 149 [arXiv:1305.3924] [INSPIRE].
D. Xie and K. Yonekura, Generalized Hitchin system, Spectral curve and \( \mathcal{N} \) = 1 dynamics, JHEP 01 (2014) 001 [arXiv:1310.0467] [INSPIRE].
D. Xie and Friends, work in progress.
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: 1307.5877
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
Xie, D. M5 brane and four dimensional \( \mathcal{N} \) = 1 theories I. J. High Energ. Phys. 2014, 154 (2014). https://doi.org/10.1007/JHEP04(2014)154
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2014)154