Abstract
We study the moduli space of 3d \( \mathcal{N} \) = 4 quiver gauge theories with unitary, orthogonal and symplectic gauge nodes, that fall into exceptional sequences. We find that both the Higgs and Coulomb branches of the moduli space factorise into decoupled sectors. Each decoupled sector is described by a single quiver gauge theory with only unitary gauge nodes. The orthosymplectic quivers serve as magnetic quivers for 5d \( \mathcal{N} \) = 1 superconformal field theories which can be engineered in type IIB string theories both with and without an O5 plane. We use this point of view to postulate the dual pairs of unitary and orthosymplectic quivers by deriving them as magnetic quivers of the 5d theory. We use this correspondence to conjecture exact highest weight generating functions for the Coulomb branch Hilbert series of the orthosymplectic quivers, and provide tests of these results by directly computing the Hilbert series for the orthosymplectic quivers in a series expansion.
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References
A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152 [hep-th/9611230] [INSPIRE].
M. Akhond, F. Carta, S. Dwivedi, H. Hayashi, S.-S. Kim and F. Yagi, Five-brane webs, Higgs branches and unitary/orthosymplectic magnetic quivers, JHEP 12 (2020) 164 [arXiv:2008.01027] [INSPIRE].
A. Bourget, S. Cabrera, J. F. Grimminger, A. Hanany and Z. Zhong, Brane Webs and Magnetic Quivers for SQCD, JHEP 03 (2020) 176 [arXiv:1909.00667] [INSPIRE].
A. Bourget, J. F. Grimminger, A. Hanany, M. Sperling, G. Zafrir and Z. Zhong, Magnetic quivers for rank 1 theories, JHEP 09 (2020) 189 [arXiv:2006.16994] [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].
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].
C. Closset, S. Schäfer-Nameki and Y.-N. Wang, Coulomb and Higgs Branches from Canonical Singularities: Part 0, JHEP 02 (2021) 003 [arXiv:2007.15600] [INSPIRE].
M. van Beest, A. Bourget, J. Eckhard and S. Schäfer-Nameki, (Symplectic) Leaves and (5d Higgs) Branches in the Poly(go)nesian Tropical Rain Forest, JHEP 11 (2020) 124 [arXiv:2008.05577] [INSPIRE].
M. Van Beest, A. Bourget, J. Eckhard and S. Schäfer-Nameki, (5d RG-flow) Trees in the Tropical Rain Forest, JHEP 03 (2021) 241 [arXiv:2011.07033] [INSPIRE].
A. Bourget, S. Giacomelli, J. F. Grimminger, A. Hanany, M. Sperling and Z. Zhong, S-fold magnetic quivers, JHEP 02 (2021) 054 [arXiv:2010.05889] [INSPIRE].
S. Cabrera, A. Hanany and F. Yagi, Tropical Geometry and Five Dimensional Higgs Branches at Infinite Coupling, JHEP 01 (2019) 068 [arXiv:1810.01379] [INSPIRE].
S. Cabrera, A. Hanany and M. Sperling, Magnetic quivers, Higgs branches, and 6d N = (1, 0) theories, JHEP 06 (2019) 071 [Erratum ibid. 07 (2019) 137] [arXiv:1904.12293] [INSPIRE].
J. Eckhard, S. Schäfer-Nameki and Y.-N. Wang, Trifectas for TN in 5d, JHEP 07 (2020) 199 [arXiv:2004.15007] [INSPIRE].
C. Closset, S. Giacomelli, S. Schäfer-Nameki and Y.-N. Wang, 5d and 4d SCFTs: Canonical Singularities, Trinions and S-Dualities, arXiv:2012.12827 [INSPIRE].
K. A. Intriligator and N. Seiberg, Mirror symmetry in three-dimensional gauge theories, Phys. Lett. B 387 (1996) 513 [hep-th/9607207] [INSPIRE].
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].
F. Benini, S. Benvenuti and Y. Tachikawa, Webs of five-branes and N = 2 superconformal field theories, JHEP 09 (2009) 052 [arXiv:0906.0359] [INSPIRE].
F. Benini, Y. Tachikawa and D. Xie, Mirrors of 3d Sicilian theories, JHEP 09 (2010) 063 [arXiv:1007.0992] [INSPIRE].
A. Collinucci and R. Valandro, A string theory realization of special unitary quivers in 3 dimensions, JHEP 11 (2020) 157 [arXiv:2008.10689] [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].
J. Gray, A. Hanany, Y.-H. He, V. Jejjala and N. Mekareeya, SQCD: A Geometric Apercu, JHEP 05 (2008) 099 [arXiv:0803.4257] [INSPIRE].
B. Feng and A. Hanany, Mirror symmetry by O3 planes, JHEP 11 (2000) 033 [hep-th/0004092] [INSPIRE].
S. Benvenuti, B. Feng, A. Hanany and Y.-H. He, Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics, JHEP 11 (2007) 050 [hep-th/0608050] [INSPIRE].
B. Feng, A. Hanany and Y.-H. He, Counting gauge invariants: The Plethystic program, JHEP 03 (2007) 090 [hep-th/0701063] [INSPIRE].
A. Hanany and R. Kalveks, Highest Weight Generating Functions for Hilbert Series, JHEP 10 (2014) 152 [arXiv:1408.4690] [INSPIRE].
O. Chacaltana and J. Distler, Tinkertoys for the DN series, JHEP 02 (2013) 110 [arXiv:1106.5410] [INSPIRE].
J. Distler, B. Ergun and F. Yan, Product SCFTs in Class-S, JHEP 02 (2021) 164 [arXiv:1711.04727] [INSPIRE].
J. Distler and B. Ergun, Product SCFTs for the E7 Theory, arXiv:1803.02425 [INSPIRE].
B. Ergun, Q. Hao, A. Neitzke and F. Yan, Factorized class S theories and surface defects, arXiv:2010.06722 [INSPIRE].
G. Zafrir, Brane webs and O5-planes, JHEP 03 (2016) 109 [arXiv:1512.08114] [INSPIRE].
O. Aharony, A. Hanany and B. Kol, Webs of (p,q) five-branes, five-dimensional field theories and grid diagrams, JHEP 01 (1998) 002 [hep-th/9710116] [INSPIRE].
O. Bergman, D. Rodríguez-Gómez and G. Zafrir, 5-Brane Webs, Symmetry Enhancement, and Duality in 5d Supersymmetric Gauge Theory, JHEP 03 (2014) 112 [arXiv:1311.4199] [INSPIRE].
E. Beratto, S. Giacomelli, N. Mekareeya and M. Sacchi, 3d mirrors of the circle reduction of twisted A2N theories of class S, JHEP 09 (2020) 161 [arXiv:2007.05019] [INSPIRE].
G. Ferlito, A. Hanany, N. Mekareeya and G. Zafrir, 3d Coulomb branch and 5d Higgs branch at infinite coupling, JHEP 07 (2018) 061 [arXiv:1712.06604] [INSPIRE].
G. Ferlito and A. Hanany, A tale of two cones: the Higgs Branch of Sp(n) theories with 2n flavours, arXiv:1609.06724 [INSPIRE].
A. Hanany and R. Kalveks, Quiver Theories for Moduli Spaces of Classical Group Nilpotent Orbits, JHEP 06 (2016) 130 [arXiv:1601.04020] [INSPIRE].
J. A. Minahan and D. Nemeschansky, An N = 2 superconformal fixed point with E6 global symmetry, Nucl. Phys. B 482 (1996) 142 [hep-th/9608047] [INSPIRE].
J. A. Minahan and D. Nemeschansky, Superconformal fixed points with E(n) global symmetry, Nucl. Phys. B 489 (1997) 24 [hep-th/9610076] [INSPIRE].
A. Hanany and N. Mekareeya, Complete Intersection Moduli Spaces in N = 4 Gauge Theories in Three Dimensions, JHEP 01 (2012) 079 [arXiv:1110.6203] [INSPIRE].
H. Hayashi, S.-S. Kim, K. Lee and F. Yagi, Discrete theta angle from an O5-plane, JHEP 11 (2017) 041 [arXiv:1707.07181] [INSPIRE].
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Akhond, M., Carta, F., Dwivedi, S. et al. Factorised 3d \( \mathcal{N} \) = 4 orthosymplectic quivers. J. High Energ. Phys. 2021, 269 (2021). https://doi.org/10.1007/JHEP05(2021)269
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DOI: https://doi.org/10.1007/JHEP05(2021)269