Abstract
We find exact relations among the sphere partition functions of three-dimensional \( \mathcal{N} \) = 4 superconformal Chern-Simons theories with circular quiver diagrams. These relations suggest new dualities in gauge theories which are the products of circular quiver gauge theories and decoupled linear quiver gauge theories. The dualities can be interpreted as simple brane transitions in the Hanany-Witten brane construction in type IIB string theory. Interestingly, the brane transitions cannot be generated by the Hanany-Witten transition or the SL (2, ℤ) transformation. Our results can be regarded as generalization and clarification of dualities implied from Weyl group symmetries of quantum curves. To obtain the exact results, we employ the supersymmetric localization technique and the Fermi gas approach.
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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].
J. de Boer, K. Hori, H. Ooguri, Y. Oz and Z. Yin, Mirror symmetry in three-dimensional theories, SL(2,Z) and D-brane moduli spaces, Nucl. Phys. B 493 (1997) 148 [hep-th/9612131] [INSPIRE].
A. Giveon and D. Kutasov, Seiberg Duality in Chern-Simons Theory, Nucl. Phys. B 812 (2009) 1 [arXiv:0808.0360] [INSPIRE].
A. Amariti, D. Forcella, C. Klare, D. Orlando and S. Reffert, The braneology of 3D dualities, J. Phys. A 48 (2015) 265401 [arXiv:1501.06571] [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].
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].
O. Aharony, O. Bergman and D.L. Jafferis, Fractional M2-branes, JHEP 11 (2008) 043 [arXiv:0807.4924] [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].
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].
M. Mariño and P. Putrov, ABJM theory as a Fermi gas, J. Stat. Mech. 1203 (2012) P03001 [arXiv:1110.4066] [INSPIRE].
N. Drukker and J. Felix, 3d mirror symmetry as a canonical transformation, JHEP 05 (2015) 004 [arXiv:1501.02268] [INSPIRE].
B. Assel, N. Drukker and J. Felix, Partition functions of 3d \( \hat{D} \)-quivers and their mirror duals from 1d free fermions, JHEP 08 (2015) 071 [arXiv:1504.07636] [INSPIRE].
M. Honda, Exact relations between M2-brane theories with and without Orientifolds, JHEP 06 (2016) 123 [arXiv:1512.04335] [INSPIRE].
M. Mariño and S. Zakany, Matrix models from operators and topological strings, Annales Henri Poincaré 17 (2016) 1075 [arXiv:1502.02958] [INSPIRE].
R. Kashaev, M. Mariño and S. Zakany, Matrix models from operators and topological strings, 2, Ann. Henri Poincaré 17 (2016) 2741 [arXiv:1505.02243] [INSPIRE].
Y. Hatsuda, ABJM on ellipsoid and topological strings, JHEP 07 (2016) 026 [arXiv:1601.02728] [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].
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].
T. Furukawa, S. Moriyama and T. Nakanishi, Brane transitions from exceptional groups, Nucl. Phys. B 969 (2021) 115477 [arXiv:2010.15402] [INSPIRE].
S. Moriyama, Spectral Theories and Topological Strings on del Pezzo Geometries, JHEP 10 (2020) 154 [arXiv:2007.05148] [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].
A. Kapustin, B. Willett and I. Yaakov, Tests of Seiberg-like dualities in three dimensions, JHEP 08 (2020) 114 [arXiv:1012.4021] [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].
M. Honda and N. Kubo, Non-perturbative tests of duality cascades in three dimensional supersymmetric gauge theories, JHEP 07 (2021) 012 [arXiv:2010.15656] [INSPIRE].
B. Assel, Hanany-Witten effect and SL(2, ℤ) dualities in matrix models, JHEP 10 (2014) 117 [arXiv:1406.5194] [INSPIRE].
N. Hama, K. Hosomichi and S. Lee, Notes on SUSY Gauge Theories on Three-Sphere, JHEP 03 (2011) 127 [arXiv:1012.3512] [INSPIRE].
M. Mariño, Lectures on localization and matrix models in supersymmetric Chern-Simons-matter theories, J. Phys. A 44 (2011) 463001 [arXiv:1104.0783] [INSPIRE].
N. Drukker, M. Mariño and P. Putrov, From weak to strong coupling in ABJM theory, Commun. Math. Phys. 306 (2011) 511 [arXiv:1007.3837] [INSPIRE].
S. Moriyama and T. Nosaka, Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach, JHEP 11 (2014) 164 [arXiv:1407.4268] [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].
M. Honda and K. Okuyama, Exact results on ABJ theory and the refined topological string, JHEP 08 (2014) 148 [arXiv:1405.3653] [INSPIRE].
Y. Imamura and K. Kimura, On the moduli space of elliptic Maxwell-Chern-Simons theories, Prog. Theor. Phys. 120 (2008) 509 [arXiv:0806.3727] [INSPIRE].
E. Witten, Quantum Field Theory and the Jones Polynomial, Commun. Math. Phys. 121 (1989) 351 [INSPIRE].
S. Moriyama and T. Nosaka, Superconformal Chern-Simons Partition Functions of Affine D-type Quiver from Fermi Gas, JHEP 09 (2015) 054 [arXiv:1504.07710] [INSPIRE].
K. Okuyama, Orientifolding of the ABJ Fermi gas, JHEP 03 (2016) 008 [arXiv:1601.03215] [INSPIRE].
S. Moriyama and T. Suyama, Orthosymplectic Chern-Simons Matrix Model and Chirality Projection, JHEP 04 (2016) 132 [arXiv:1601.03846] [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].
T. Nosaka, SU(N) q-Toda equations from mass deformed ABJM theory, JHEP 06 (2021) 060 [arXiv:2012.07211] [INSPIRE].
S. Moriyama and Y. Yamada, Quantum Representation of Affine Weyl Groups and Associated Quantum Curves, SIGMA 17 (2021) 076 [arXiv:2104.06661] [INSPIRE].
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Kubo, N. 3d dualities with decoupled sectors and brane transitions. J. High Energ. Phys. 2022, 80 (2022). https://doi.org/10.1007/JHEP05(2022)080
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DOI: https://doi.org/10.1007/JHEP05(2022)080