Abstract
The Higgs branch of minimally supersymmetric five dimensional SQCD theories increases in a significant way at the UV fixed point when the inverse gauge coupling is tuned to zero. It has been a long standing problem to figure out how, and to find an exact description of this Higgs branch. This paper solves this problem in an elegant way by proposing that the Coulomb branches of three dimensional \( \mathcal{N}=4 \) supersymmetric quiver gauge theories, named “Exceptional Sequences”, provide the solution to the problem. Thus, once again, 3d \( \mathcal{N}=4 \) Coulomb branches prove to be useful tools in solving problems in higher dimensions. Gauge invariant operators on the 5d side consist of classical objects such as mesons, baryons and gaugino bilinears, and non perturbative objects such as instanton operators with or without baryon number. On the 3d side we have classical objects such as Casimir invariants and non perturbative objects such as monopole operators, bare or dressed. The duality map works in a very interesting way.
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References
N. Seiberg, Five-dimensional SUSY field theories, nontrivial fixed points and string dynamics, Phys. Lett. B 388 (1996) 753 [hep-th/9608111] [INSPIRE].
D.R. Morrison and N. Seiberg, Extremal transitions and five-dimensional supersymmetric field theories, Nucl. Phys. B 483 (1997) 229 [hep-th/9609070] [INSPIRE].
K.A. Intriligator, D.R. Morrison and N. Seiberg, Five-dimensional supersymmetric gauge theories and degenerations of Calabi-Yau spaces, Nucl. Phys. B 497 (1997) 56 [hep-th/9702198] [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. DeWolfe, A. Hanany, A. Iqbal and E. Katz, Five-branes, seven-branes and five-dimensional E(n) field theories, JHEP 03 (1999) 006 [hep-th/9902179] [INSPIRE].
H.-C. Kim, S.-S. Kim and K. Lee, 5-dim Superconformal Index with Enhanced En Global Symmetry, JHEP 10 (2012) 142 [arXiv:1206.6781] [INSPIRE].
D. Bashkirov, A comment on the enhancement of global symmetries in superconformal SU(2) gauge theories in 5D, arXiv:1211.4886 [INSPIRE].
L. Bao, V. Mitev, E. Pomoni, M. Taki and F. Yagi, Non-Lagrangian Theories from Brane Junctions, JHEP 01 (2014) 175 [arXiv:1310.3841] [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].
G. Zafrir, Duality and enhancement of symmetry in 5d gauge theories, JHEP 12 (2014) 116 [arXiv:1408.4040] [INSPIRE].
V. Mitev, E. Pomoni, M. Taki and F. Yagi, Fiber-Base Duality and Global Symmetry Enhancement, JHEP 04 (2015) 052 [arXiv:1411.2450] [INSPIRE].
Y. Tachikawa, Instanton operators and symmetry enhancement in 5d supersymmetric gauge theories, PTEP 2015 (2015) 043B06 [arXiv:1501.01031] [INSPIRE].
H. Hayashi, S.-S. Kim, K. Lee, M. Taki and F. Yagi, A new 5d description of 6d D-type minimal conformal matter, JHEP 08 (2015) 097 [arXiv:1505.04439] [INSPIRE].
K. Yonekura, Instanton operators and symmetry enhancement in 5d supersymmetric quiver gauge theories, JHEP 07 (2015) 167 [arXiv:1505.04743] [INSPIRE].
D. Gaiotto and H.-C. Kim, Duality walls and defects in 5d \( \mathcal{N}=1 \) theories, JHEP 01 (2017) 019 [arXiv:1506.03871] [INSPIRE].
O. Bergman and G. Zafrir, 5d fixed points from brane webs and O7-planes, JHEP 12 (2015) 163 [arXiv:1507.03860] [INSPIRE].
A. Hanany and R. Kalveks, Quiver Theories and Formulae for Nilpotent Orbits of Exceptional Algebras, JHEP 11 (2017) 126 [arXiv:1709.05818] [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].
O. Aharony and A. Hanany, Branes, superpotentials and superconformal fixed points, Nucl. Phys. B 504 (1997) 239 [hep-th/9704170] [INSPIRE].
S. Cremonesi, G. Ferlito, A. Hanany and N. Mekareeya, Instanton Operators and the Higgs Branch at Infinite Coupling, JHEP 04 (2017) 042 [arXiv:1505.06302] [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].
N. Lambert, C. Papageorgakis and M. Schmidt-Sommerfeld, Instanton Operators in Five-Dimensional Gauge Theories, JHEP 03 (2015) 019 [arXiv:1412.2789] [INSPIRE].
O. Bergman and D. Rodriguez-Gomez, A Note on Instanton Operators, Instanton Particles and Supersymmetry, JHEP 05 (2016) 068 [arXiv:1601.00752] [INSPIRE].
Y. Namikawa, A characterization of nilpotent orbit closures among symplectic singularities, arXiv:1603.06105.
S. Cabrera and A. Hanany, Branes and the Kraft-Procesi Transition, JHEP 11 (2016) 175 [arXiv:1609.07798] [INSPIRE].
S. Cremonesi, G. Ferlito, A. Hanany and N. Mekareeya, Coulomb Branch and The Moduli Space of Instantons, JHEP 12 (2014) 103 [arXiv:1408.6835] [INSPIRE].
P.C. Argyres and M.R. Douglas, New phenomena in SU(3) supersymmetric gauge theory, Nucl. Phys. B 448 (1995) 93 [hep-th/9505062] [INSPIRE].
S. Cecotti, A. Neitzke and C. Vafa, R-Twisting and 4d/2d Correspondences, arXiv:1006.3435 [INSPIRE].
P. Boalch, Simply-laced isomonodromy systems, Publ. Math. IHES 116 (2012) 1, [arXiv:1107.0874].
D. Xie, General Argyres-Douglas Theory, JHEP 01 (2013) 100 [arXiv:1204.2270] [INSPIRE].
M. Del Zotto and A. Hanany, Complete Graphs, Hilbert Series and the Higgs branch of the 4d \( \mathcal{N}=2\left({A}_n,{A}_m\right) \) SCFTs, Nucl. Phys. B 894 (2015) 439 [arXiv:1403.6523] [INSPIRE].
N. Mekareeya, K. Ohmori, Y. Tachikawa and G. Zafrir, E 8 instantons on type-A ALE spaces and supersymmetric field theories, JHEP 09 (2017) 144 [arXiv:1707.04370] [INSPIRE].
N. Mekareeya, K. Ohmori, H. Shimizu and A. Tomasiello, Small instanton transitions for M5 fractions, JHEP 10 (2017) 055 [arXiv:1707.05785] [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].
S. Cremonesi, A. Hanany, N. Mekareeya and A. Zaffaroni, Coulomb branch Hilbert series and Hall-Littlewood polynomials, JHEP 09 (2014) 178 [arXiv:1403.0585] [INSPIRE].
S. Cremonesi, A. Hanany, N. Mekareeya and A. Zaffaroni, Coulomb branch Hilbert series and Three Dimensional Sicilian Theories, JHEP 09 (2014) 185 [arXiv:1403.2384] [INSPIRE].
A. Hanany and R. Kalveks, Highest Weight Generating Functions for Hilbert Series, JHEP 10 (2014) 152 [arXiv:1408.4690] [INSPIRE].
T. Kobayashi, Geometry of multiplicity-free representations of GL(n), visible actions on flag varieties, and triunity, Acta Appl. Math. 81 (2004) 129.
A. Hanany and R. Kalveks, Quiver Theories for Moduli Spaces of Classical Group Nilpotent Orbits, JHEP 06 (2016) 130 [arXiv:1601.04020] [INSPIRE].
S.-S. Kim, M. Taki and F. Yagi, Tao Probing the End of the World, PTEP 2015 (2015) 083B02 [arXiv:1504.03672] [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].
A. Hanany and R. Kalveks, Construction and Deconstruction of Single Instanton Hilbert Series, JHEP 12 (2015) 118 [arXiv:1509.01294] [INSPIRE].
A. Hanany and A. Pini, HWG for Coulomb branch of 3d Sicilian theory mirrors, arXiv:1707.09784 [INSPIRE].
O. Bergman and G. Zafrir, 5d fixed points from brane webs and O7-planes, JHEP 12 (2015) 163 [arXiv:1507.03860] [INSPIRE].
F. Benini, Y. Tachikawa and D. Xie, Mirrors of 3d Sicilian theories, JHEP 09 (2010) 063 [arXiv:1007.0992] [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].
O. Chacaltana and J. Distler, Tinkertoys for Gaiotto Duality, JHEP 11 (2010) 099 [arXiv:1008.5203] [INSPIRE].
K. Ohmori, H. Shimizu, Y. Tachikawa and K. Yonekura, 6d \( \mathcal{N}=\left(1,0\right) \) theories on S 1 /T 2 and class S theories: part II, JHEP 12 (2015) 131 [arXiv:1508.00915] [INSPIRE].
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Ferlito, G., Hanany, A., Mekareeya, N. et al. 3d Coulomb branch and 5d Higgs branch at infinite coupling. J. High Energ. Phys. 2018, 61 (2018). https://doi.org/10.1007/JHEP07(2018)061
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DOI: https://doi.org/10.1007/JHEP07(2018)061