Abstract
It has been conjectured that duality cascade occurs in the \( \mathcal{N} \) = 3 supersymmetric Yang-Mills Chern-Simons theory with the gauge group U(N)k × U(N + M)−k coupled to two bi-fundamental hypermultiplets. The brane picture suggests that this duality cascade can be generalized to a class of 3d \( \mathcal{N} \) = 3 supersymmetric quiver gauge theories coming from so-called Hanany-Witten type brane configurations. In this paper we perform non-perturbative tests of the duality cascades using supersymmetry localization. We focus on S3 partition functions and prove predictions from the duality cascades. We also discuss that our result can be applied to generate new dualities for more general theories which include less supersymmetric theories and theories without brane constructions.
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References
N. Seiberg, Electric-magnetic duality in supersymmetric non-Abelian gauge theories, Nucl. Phys. B 435 (1995) 129 [hep-th/9411149] [INSPIRE].
I.R. Klebanov and M.J. Strassler, Supergravity and a confining gauge theory: Duality cascades and chi SB resolution of naked singularities, JHEP 08 (2000) 052 [hep-th/0007191] [INSPIRE].
M.J. Strassler, The Duality cascade, in Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 2003): Recent Trends in String Theory, (2005) [DOI] [hep-th/0505153] [INSPIRE].
S.B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66 (2002) 106006 [hep-th/0105097] [INSPIRE].
S. Kachru, R. Kallosh, A.D. Linde and S.P. Trivedi, de Sitter vacua in string theory, Phys. Rev. D 68 (2003) 046005 [hep-th/0301240] [INSPIRE].
S. Kachru, R. Kallosh, A.D. Linde, J.M. Maldacena, L.P. McAllister and S.P. Trivedi, Towards inflation in string theory, JCAP 10 (2003) 013 [hep-th/0308055] [INSPIRE].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
O. Aharony, O. Bergman and D.L. Jafferis, Fractional M2-branes, JHEP 11 (2008) 043 [arXiv:0807.4924] [INSPIRE].
A. Giveon and D. Kutasov, Seiberg Duality in Chern-Simons Theory, Nucl. Phys. B 812 (2009) 1 [arXiv:0808.0360] [INSPIRE].
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].
A. Kapustin, B. Willett and I. Yaakov, Tests of Seiberg-like dualities in three dimensions, JHEP 08 (2020) 114 [arXiv:1012.4021] [INSPIRE].
H. Awata, S. Hirano and M. Shigemori, The Partition Function of ABJ Theory, PTEP 2013 (2013) 053B04 [arXiv:1212.2966] [INSPIRE].
M. Honda, Direct derivation of “mirror” ABJ partition function, JHEP 12 (2013) 046 [arXiv:1310.3126] [INSPIRE].
S. Matsumoto and S. Moriyama, ABJ Fractional Brane from ABJM Wilson Loop, JHEP 03 (2014) 079 [arXiv:1310.8051] [INSPIRE].
M. Honda and K. Okuyama, Exact results on ABJ theory and the refined topological string, JHEP 08 (2014) 148 [arXiv:1405.3653] [INSPIRE].
S. Hirano, K. Nii and M. Shigemori, ABJ Wilson loops and Seiberg duality, PTEP 2014 (2014) 113B04 [arXiv:1406.4141] [INSPIRE].
O. Aharony, A. Hashimoto, S. Hirano and P. Ouyang, D-brane Charges in Gravitational Duals of 2+1 Dimensional Gauge Theories and Duality Cascades, JHEP 01 (2010) 072 [arXiv:0906.2390] [INSPIRE].
J. Evslin and S. Kuperstein, ABJ(M) and Fractional M2’s with Fractional M2 Charge, JHEP 12 (2009) 016 [arXiv:0906.2703] [INSPIRE].
D. Gaiotto and E. Witten, Janus Configurations, Chern-Simons Couplings, And The theta-Angle in N = 4 Super Yang-Mills Theory, JHEP 06 (2010) 097 [arXiv:0804.2907] [INSPIRE].
K. Hosomichi, K.-M. Lee, S. Lee, S. Lee and J. Park, N = 4 Superconformal Chern-Simons Theories with Hyper and Twisted Hyper Multiplets, JHEP 07 (2008) 091 [arXiv:0805.3662] [INSPIRE].
Y. Imamura and K. Kimura, N = 4 Chern-Simons theories with auxiliary vector multiplets, JHEP 10 (2008) 040 [arXiv:0807.2144] [INSPIRE].
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [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].
T. Kitao, K. Ohta and N. Ohta, Three-dimensional gauge dynamics from brane configurations with (p,q)-fivebrane, Nucl. Phys. B 539 (1999) 79 [hep-th/9808111] [INSPIRE].
O. Bergman and A. Fayyazuddin, String junction transitions in the moduli space of N = 2 SYM, Nucl. Phys. B 535 (1998) 139 [hep-th/9806011] [INSPIRE].
O. Bergman, A. Hanany, A. Karch and B. Kol, Branes and supersymmetry breaking in three-dimensional gauge theories, JHEP 10 (1999) 036 [hep-th/9908075] [INSPIRE].
K. Dasgupta and S. Mukhi, Brane constructions, fractional branes and Anti-de Sitter domain walls, JHEP 07 (1999) 008 [hep-th/9904131] [INSPIRE].
F. Cachazo, B. Fiol, K.A. Intriligator, S. Katz and C. Vafa, A Geometric unification of dualities, Nucl. Phys. B 628 (2002) 3 [hep-th/0110028] [INSPIRE].
A. Kapustin, B. Willett and I. Yaakov, Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter, JHEP 03 (2010) 089 [arXiv:0909.4559] [INSPIRE].
N. Hama, K. Hosomichi and S. Lee, Notes on SUSY Gauge Theories on Three-Sphere, JHEP 03 (2011) 127 [arXiv:1012.3512] [INSPIRE].
D.L. Jafferis, The Exact Superconformal R-Symmetry Extremizes Z, JHEP 05 (2012) 159 [arXiv:1012.3210] [INSPIRE].
B. Assel, Hanany-Witten effect and SL(2, ℤ) dualities in matrix models, JHEP 10 (2014) 117 [arXiv:1406.5194] [INSPIRE].
S. Benvenuti and S. Pasquetti, 3D-partition functions on the sphere: exact evaluation and mirror symmetry, JHEP 05 (2012) 099 [arXiv:1105.2551] [INSPIRE].
D.R. Gulotta, C.P. Herzog and S.S. Pufu, From Necklace Quivers to the F-theorem, Operator Counting, and T(U(N)), JHEP 12 (2011) 077 [arXiv:1105.2817] [INSPIRE].
T. Nishioka, Y. Tachikawa and M. Yamazaki, 3d Partition Function as Overlap of Wavefunctions, JHEP 08 (2011) 003 [arXiv:1105.4390] [INSPIRE].
M. Mariño and P. Putrov, ABJM theory as a Fermi gas, J. Stat. Mech. 1203 (2012) P03001 [arXiv:1110.4066] [INSPIRE].
S. Moriyama and T. Suyama, Instanton Effects in Orientifold ABJM Theory, JHEP 03 (2016) 034 [arXiv:1511.01660] [INSPIRE].
S. Moriyama and T. Suyama, Orthosymplectic Chern-Simons Matrix Model and Chirality Projection, JHEP 04 (2016) 132 [arXiv:1601.03846] [INSPIRE].
S. Moriyama and T. Nosaka, Orientifold ABJM Matrix Model: Chiral Projections and Worldsheet Instantons, JHEP 06 (2016) 068 [arXiv:1603.00615] [INSPIRE].
N. Kubo and S. Moriyama, Hanany-Witten Transition in Quantum Curves, JHEP 12 (2019) 101 [arXiv:1907.04971] [INSPIRE].
N. Kubo, Fermi gas approach to general rank theories and quantum curves, JHEP 10 (2020) 158 [arXiv:2007.08602] [INSPIRE].
M. Fujitsuka, M. Honda and Y. Yoshida, Higgs branch localization of 3d N = 2 theories, PTEP 2014 (2014) 123B02 [arXiv:1312.3627] [INSPIRE].
F. Benini and W. Peelaers, Higgs branch localization in three dimensions, JHEP 05 (2014) 030 [arXiv:1312.6078] [INSPIRE].
K. Hosomichi, K.-M. Lee, S. Lee, S. Lee and J. Park, N = 5, 6 Superconformal Chern-Simons Theories and M2-branes on Orbifolds, JHEP 09 (2008) 002 [arXiv:0806.4977] [INSPIRE].
R. Argurio and M. Bertolini, Orientifolds and duality cascades: confinement before the wall, JHEP 02 (2018) 149 [arXiv:1711.08983] [INSPIRE].
A. Karasik and Z. Komargodski, The Bi-Fundamental Gauge Theory in 3+1 Dimensions: The Vacuum Structure and a Cascade, JHEP 05 (2019) 144 [arXiv:1904.09551] [INSPIRE].
R. Kashaev, M. Mariño and S. Zakany, Matrix models from operators and topological strings, 2, Annales Henri Poincaré 17 (2016) 2741 [arXiv:1505.02243] [INSPIRE].
G. Bonelli, A. Grassi and A. Tanzini, Quantum curves and q-deformed Painlevé equations, Lett. Math. Phys. 109 (2019) 1961 [arXiv:1710.11603] [INSPIRE].
N. Kubo, S. Moriyama and T. Nosaka, Symmetry Breaking in Quantum Curves and Super Chern-Simons Matrix Models, JHEP 01 (2019) 210 [arXiv:1811.06048] [INSPIRE].
S. Moriyama, Spectral Theories and Topological Strings on del Pezzo Geometries, JHEP 10 (2020) 154 [arXiv:2007.05148] [INSPIRE].
T. Furukawa, S. Moriyama and T. Nakanishi, Brane Transitions from Exceptional Groups, arXiv:2010.15402 [INSPIRE].
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Honda, M., Kubo, N. Non-perturbative tests of duality cascades in three dimensional supersymmetric gauge theories. J. High Energ. Phys. 2021, 12 (2021). https://doi.org/10.1007/JHEP07(2021)012
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DOI: https://doi.org/10.1007/JHEP07(2021)012