Abstract
A generalized Hitchin equation was proposed as the BPS equation for a large class of four dimensional \( \mathcal{N} \) = 1 theories engineered using M5 branes. In this paper, we show how to write down the spectral curve for the moduli space of generalized Hitchin equations, and extract interesting \( \mathcal{N} \) = 1 dynamics out of it, such as deformed modui space, chiral ring relation, SUSY breaking, etc. Holomorphy plays a crucial role in our construction.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys. B 426 (1994) 19 [Erratum ibid. B 430 (1994) 485] [hep-th/9407087] [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].
E. Witten, Solutions of four-dimensional field theories via M-theory, Nucl. Phys. B 500 (1997) 3 [hep-th/9703166] [INSPIRE].
R. Donagi and E. Witten, Supersymmetric Yang-Mills theory and integrable systems, Nucl. Phys. B 460 (1996) 299 [hep-th/9510101] [INSPIRE].
A. Kapustin, Solution of N = 2 gauge theories via compactification to three-dimensions, Nucl. Phys. B 534 (1998) 531 [hep-th/9804069] [INSPIRE].
D. Gaiotto, G.W. Moore and A. Neitzke, Wall-crossing, Hitchin systems and the WKB approximation, arXiv:0907.3987 [INSPIRE].
K.A. Intriligator and N. Seiberg, Phases of N = 1 supersymmetric gauge theories in four-dimensions, Nucl. Phys. B 431 (1994) 551 [hep-th/9408155] [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].
E. Witten, Branes and the dynamics of QCD, Nucl. Phys. B 507 (1997) 658 [hep-th/9706109] [INSPIRE].
A. Giveon and D. Kutasov, Brane dynamics and gauge theory, Rev. Mod. Phys. 71 (1999) 983 [hep-th/9802067] [INSPIRE].
D. Xie, M5 brane and four dimensional N = 1 theories I, 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].
F. Benini, Y. Tachikawa and B. Wecht, Sicilian gauge theories and N = 1 dualities, JHEP 01 (2010) 088 [arXiv:0909.1327] [INSPIRE].
Y. Tachikawa and K. Yonekura, N = 1 curves for trifundamentals, JHEP 07 (2011) 025 [arXiv:1105.3215] [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 superconformal index of N = 1 class S fixed points, 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].
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].
K. Maruyoshi, Y. Tachikawa, W. Yan and K. Yonekura, N = 1 dynamics with T N theory, JHEP 10 (2013) 010 [arXiv:1305.5250] [INSPIRE].
I. Bah and N. Bobev, Linear quivers and N = 1 SCFTs from M5-branes, arXiv:1307.7104 [INSPIRE].
K. Maruyoshi, Y. Tachikawa, W. Yan and K. Yonekura, Dynamical supersymmetry breaking with T N theory, arXiv:1308.0064 [INSPIRE].
G. Bonelli, S. Giacomelli, K. Maruyoshi and A. Tanzini, N = 1 geometries via M-theory, JHEP 10 (2013) 227 [arXiv:1307.7703] [INSPIRE].
N. Seiberg, Naturalness versus supersymmetric nonrenormalization theorems, Phys. Lett. B 318 (1993) 469 [hep-ph/9309335] [INSPIRE].
A. Beauville, M. Narasimhan and S. Ramanan, Spectral curves and the generalised theta divisor, J. Reine Angew. Math. 398 (1989) 169.
E. Markman, Spectral curves and integrable systems, Composit. Math. 93 (1994) 255.
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].
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. de Boer, K. Hori, H. Ooguri and Y. Oz, Branes and dynamical supersymmetry breaking, Nucl. Phys. B 522 (1998) 20 [hep-th/9801060] [INSPIRE].
D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].
S. Rayan and D. Xie, 6d self-dual equation on Riemann surface, work in progress.
D. Nanopoulos and D. Xie, Hitchin equation, irregular singularity and N = 2 asymptotical free theories, arXiv:1005.1350 [INSPIRE].
I. Affleck, M. Dine and N. Seiberg, Dynamical supersymmetry breaking in supersymmetric QCD, Nucl. Phys. B 241 (1984) 493 [INSPIRE].
K. Yonekura, Supersymmetric gauge theory, (2, 0) theory and twisted 5d super-Yang-Mills, arXiv:1310.7943 [INSPIRE].
K.-I. Izawa and T. Yanagida, Dynamical supersymmetry breaking in vector-like gauge theories, Prog. Theor. Phys. 95 (1996) 829 [hep-th/9602180] [INSPIRE].
K.A. Intriligator and S.D. Thomas, Dynamical supersymmetry breaking on quantum moduli spaces, Nucl. Phys. B 473 (1996) 121 [hep-th/9603158] [INSPIRE].
D. Xie, General Argyres-Douglas theory, JHEP 01 (2013) 100 [arXiv:1204.2270] [INSPIRE].
N. Seiberg, Electric-magnetic duality in supersymmetric non-Abelian gauge theories, Nucl. Phys. B 435 (1995) 129 [hep-th/9411149] [INSPIRE].
D. Gaiotto, S. Gukov and N. Seiberg, Surface defects and resolvents, JHEP 09 (2013) 070 [arXiv:1307.2578] [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: 1310.0467
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Xie, D., Yonekura, K. Generalized Hitchin system, spectral curve and \( \mathcal{N} \) =1 dynamics. J. High Energ. Phys. 2014, 1 (2014). https://doi.org/10.1007/JHEP01(2014)001
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2014)001