Abstract
We propose magnetic quivers for partial implosion spaces. Such partial implosions involve a choice of parabolic subgroup, with the Borel subgroup corresponding to the standard implosion. In the subregular case we test the conjecture by verifying that reduction by the Levi group gives the appropriate nilpotent orbit closure. In the case of a parabolic corresponding to a hook diagram we are also able to carry out this verification provided we work at nonzero Fayet-Iliopoulos parameters.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Dancer, A. Hanany and F. Kirwan, Symplectic duality and implosions, Adv. Theor. Math. Phys. 25 (2021) 1367 [arXiv:2004.09620] [INSPIRE].
A. Bourget, A. Dancer, J.F. Grimminger, A. Hanany, F. Kirwan and Z. Zhong, Orthosymplectic implosions, JHEP 08 (2021) 012 [arXiv:2103.05458] [INSPIRE].
N.J. Hitchin, A. Karlhede, U. Lindström and M. Roček, HyperKähler Metrics and Supersymmetry, Commun. Math. Phys. 108 (1987) 535 [INSPIRE].
S. Cremonesi, A. Hanany and A. Zaffaroni, Monopole operators and Hilbert series of Coulomb branches of 3d \( \mathcal{N} \) = 4 gauge theories, JHEP 01 (2014) 005 [arXiv:1309.2657] [INSPIRE].
M. Bullimore, T. Dimofte and D. Gaiotto, The Coulomb Branch of 3d \( \mathcal{N} \) = 4 Theories, Commun. Math. Phys. 354 (2017) 671 [arXiv:1503.04817] [INSPIRE].
H. Nakajima, Towards a mathematical definition of Coulomb branches of 3-dimensional \( \mathcal{N} \) = 4 gauge theories, I, Adv. Theor. Math. Phys. 20 (2016) 595 [arXiv:1503.03676] [INSPIRE].
A. Braverman, M. Finkelberg and H. Nakajima, Towards a mathematical definition of Coulomb branches of 3-dimensional \( \mathcal{N} \) = 4 gauge theories, II, Adv. Theor. Math. Phys. 22 (2018) 1071 [arXiv:1601.03586] [INSPIRE].
A. Bourget, J.F. Grimminger, A. Hanany, R. Kalveks and Z. Zhong, Higgs Branches of U/SU Quivers via Brane Locking, arXiv:2111.04745 [INSPIRE].
I. Yaakov, Redeeming Bad Theories, JHEP 11 (2013) 189 [arXiv:1303.2769] [INSPIRE].
B. Assel and S. Cremonesi, The Infrared Physics of Bad Theories, SciPost Phys. 3 (2017) 024 [arXiv:1707.03403] [INSPIRE].
A. Bourget et al., The Higgs mechanism — Hasse diagrams for symplectic singularities, JHEP 01 (2020) 157 [arXiv:1908.04245] [INSPIRE].
N. Seiberg, Electric-magnetic duality in supersymmetric nonAbelian gauge theories, Nucl. Phys. B 435 (1995) 129 [hep-th/9411149] [INSPIRE].
O. Aharony, IR duality in d = 3 N = 2 supersymmetric USp(2Nc) and U(Nc) gauge theories, Phys. Lett. B 404 (1997) 71 [hep-th/9703215] [INSPIRE].
A. Kapustin, Seiberg-like duality in three dimensions for orthogonal gauge groups, arXiv:1104.0466 [INSPIRE].
A. Dancer, F. Kirwan and A. Swann, Implosion for hyperkähler manifolds, Compos. Math. 149 (2013) 1592.
F. Kirwan, Symplectic implosion and nonreductive quotients, in Geometric aspects of analysis and mechanics, pp. 213–256, Progr. Math., vol. 292, Birkhauser/Springer, New York, U.S.A. (2011).
D. Collingwood and W. McGovern, Nilpotent orbits in semisimple Lie algebras, van Nostrand Reinhold (1993).
H. Nakajima, Introduction to a provisional mathematical definition of Coulomb branches of 3-dimensional N = 4 gauge theories, in Modern geometry: a celebration of the work of Simon Donaldson, pp. 193–211, Proc. Sympos. Pure Math., vol. 99, Amer. Math. Soc., Providence, RI, U.S.A. (2018).
P. Boalch, Irregular connections and Kac-Moody root systems, arXiv:0806.1050.
A. Hanany and R. Kalveks, Quiver Theories for Moduli Spaces of Classical Group Nilpotent Orbits, JHEP 06 (2016) 130 [arXiv:1601.04020] [INSPIRE].
A. Bourget, J.F. Grimminger, A. Hanany, R. Kalveks, M. Sperling and Z. Zhong, Magnetic Lattices for Orthosymplectic Quivers, JHEP 12 (2020) 092 [arXiv:2007.04667] [INSPIRE].
A. Bourget, J.F. Grimminger, A. Hanany, M. Sperling and Z. Zhong, Magnetic Quivers from Brane Webs with O5 Planes, JHEP 07 (2020) 204 [arXiv:2004.04082] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2112.10825
Rights and permissions
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.
About this article
Cite this article
Bourget, A., Dancer, A., Grimminger, J.F. et al. Partial implosions and quivers. J. High Energ. Phys. 2022, 49 (2022). https://doi.org/10.1007/JHEP07(2022)049
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2022)049