Abstract
It was known that quantum curves and super Chern-Simons matrix models correspond to each other. From the viewpoint of symmetry, the algebraic curve of genus one, called the del Pezzo curve, enjoys symmetry of the exceptional algebra, while the super Chern-Simons matrix model is described by the free energy of topological strings on the del Pezzo background with the symmetry broken. We study the symmetry breaking of the quantum cousin of the algebraic curve and reproduce the results in the super Chern-Simons matrix model.
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M. Aganagic, R. Dijkgraaf, A. Klemm, M. Mariño and C. Vafa, Topological strings and integrable hierarchies, Commun. Math. Phys. 261 (2006) 451 [hep-th/0312085] [INSPIRE].
M. Aganagic, M.C.N. Cheng, R. Dijkgraaf, D. Krefl and C. Vafa, Quantum Geometry of Refined Topological Strings, JHEP 11 (2012) 019 [arXiv:1105.0630] [INSPIRE].
N.A. Nekrasov and S.L. Shatashvili, Quantization of Integrable Systems and Four Dimensional Gauge Theories, in Proceedings, 16th International Congress on Mathematical Physics (ICMP09): Prague, Czech Republic, August 3–8, 2009, pp. 265–289, arXiv:0908.4052 [INSPIRE].
A. Mironov and A. Morozov, Nekrasov Functions and Exact Bohr-Zommerfeld Integrals, JHEP 04 (2010) 040 [arXiv:0910.5670] [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].
M. Mariño and P. Putrov, ABJM theory as a Fermi gas, J. Stat. Mech. 1203 (2012) P03001 [arXiv:1110.4066] [INSPIRE].
M. Mariño and P. Putrov, Exact Results in ABJM Theory from Topological Strings, JHEP 06 (2010) 011 [arXiv:0912.3074] [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].
C.P. Herzog, I.R. Klebanov, S.S. Pufu and T. Tesileanu, Multi-Matrix Models and Tri-Sasaki Einstein Spaces, Phys. Rev. D 83 (2011) 046001 [arXiv:1011.5487] [INSPIRE].
N. Drukker, M. Mariño and P. Putrov, Nonperturbative aspects of ABJM theory, JHEP 11 (2011) 141 [arXiv:1103.4844] [INSPIRE].
H. Fuji, S. Hirano and S. Moriyama, Summing Up All Genus Free Energy of ABJM Matrix Model, JHEP 08 (2011) 001 [arXiv:1106.4631] [INSPIRE].
M. Hanada, M. Honda, Y. Honma, J. Nishimura, S. Shiba and Y. Yoshida, Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant, JHEP 05 (2012) 121 [arXiv:1202.5300] [INSPIRE].
Y. Hatsuda, S. Moriyama and K. Okuyama, Exact Results on the ABJM Fermi Gas, JHEP 10 (2012) 020 [arXiv:1207.4283] [INSPIRE].
P. Putrov and M. Yamazaki, Exact ABJM Partition Function from TBA, Mod. Phys. Lett. A 27 (2012) 1250200 [arXiv:1207.5066] [INSPIRE].
Y. Hatsuda, S. Moriyama and K. Okuyama, Instanton Effects in ABJM Theory from Fermi Gas Approach, JHEP 01 (2013) 158 [arXiv:1211.1251] [INSPIRE].
F. Calvo and M. Mariño, Membrane instantons from a semiclassical TBA, JHEP 05 (2013) 006 [arXiv:1212.5118] [INSPIRE].
Y. Hatsuda, S. Moriyama and K. Okuyama, Instanton Bound States in ABJM Theory, JHEP 05 (2013) 054 [arXiv:1301.5184] [INSPIRE].
Y. Hatsuda, M. Mariño, S. Moriyama and K. Okuyama, Non-perturbative effects and the refined topological string, JHEP 09 (2014) 168 [arXiv:1306.1734] [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].
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].
M. Honda and S. Moriyama, Instanton Effects in Orbifold ABJM Theory, JHEP 08 (2014) 091 [arXiv:1404.0676] [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].
S. Moriyama and T. Nosaka, ABJM membrane instanton from a pole cancellation mechanism, Phys. Rev. D 92 (2015) 026003 [arXiv:1410.4918] [INSPIRE].
S. Moriyama and T. Nosaka, Exact Instanton Expansion of Superconformal Chern-Simons Theories from Topological Strings, JHEP 05 (2015) 022 [arXiv:1412.6243] [INSPIRE].
Y. Hatsuda, M. Honda and K. Okuyama, Large N non-perturbative effects in \( \mathcal{N} \) = 4 superconformal Chern-Simons theories, JHEP 09 (2015) 046 [arXiv:1505.07120] [INSPIRE].
S. Moriyama, S. Nakayama and T. Nosaka, Instanton Effects in Rank Deformed Superconformal Chern-Simons Theories from Topological Strings, JHEP 08 (2017) 003 [arXiv:1704.04358] [INSPIRE].
S. Moriyama, T. Nosaka and K. Yano, Superconformal Chern-Simons Theories from del Pezzo Geometries, JHEP 11 (2017) 089 [arXiv:1707.02420] [INSPIRE].
S. Moriyama and T. Suyama, Instanton Effects in Orientifold ABJM Theory, JHEP 03 (2016) 034 [arXiv:1511.01660] [INSPIRE].
M. Honda, Exact relations between M2-brane theories with and without Orientifolds, JHEP 06 (2016) 123 [arXiv:1512.04335] [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].
S. Moriyama and T. Nosaka, Orientifold ABJM Matrix Model: Chiral Projections and Worldsheet Instantons, JHEP 06 (2016) 068 [arXiv:1603.00615] [INSPIRE].
A. Grassi, Y. Hatsuda and M. Mariño, Topological Strings from Quantum Mechanics, Annales Henri Poincaré 17 (2016) 3177 [arXiv:1410.3382] [INSPIRE].
K. Okuyama and S. Zakany, TBA-like integral equations from quantized mirror curves, JHEP 03 (2016) 101 [arXiv:1512.06904] [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, Annales Henri Poincaré 17 (2016) 2741 [arXiv:1505.02243] [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. Kubo and S. Moriyama, Two-Point Functions in ABJM Matrix Model, JHEP 05 (2018) 181 [arXiv:1803.07161] [INSPIRE].
D.R. Gulotta, J.P. Ang and C.P. Herzog, Matrix Models for Supersymmetric Chern-Simons Theories with an ADE Classification, JHEP 01 (2012) 132 [arXiv:1111.1744] [INSPIRE].
B. Assel, N. Drukker and J. Felix, Partition functions of 3d \( \widehat{D} \) -quivers and their mirror duals from 1d free fermions, JHEP 08 (2015) 071 [arXiv:1504.07636] [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].
Y. Imamura and K. Kimura, N = 4 Chern-Simons theories with auxiliary vector multiplets, JHEP 10 (2008) 040 [arXiv:0807.2144] [INSPIRE].
M.-X. Huang, A. Klemm and M. Poretschkin, Refined stable pair invariants for E-, M- and [p, q]-strings, JHEP 11 (2013) 112 [arXiv:1308.0619] [INSPIRE].
K. Kajiwara, M. Noumi and Y. Yamada, Geometric Aspects of Painlevé Equations, J. Phys. A 50 (2017) 073001 [arXiv:1509.08186].
N. Kubo, S. Moriyama and T. Nosaka, work in progress.
S.-S. Kim and F. Yagi, 5d E n Seiberg-Witten curve via toric-like diagram, JHEP 06 (2015) 082 [arXiv:1411.7903] [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].
S. Codesido, A. Grassi and M. Mariño, Spectral Theory and Mirror Curves of Higher Genus, Annales Henri Poincaré 18 (2017) 559 [arXiv:1507.02096] [INSPIRE].
G. Bonelli, A. Grassi and A. Tanzini, Quantum curves and q-deformed Painlevé equations, arXiv:1710.11603 [INSPIRE].
A. Grassi and J. Gu, Argyres-Douglas theories, Painlevé II and quantum mechanics, arXiv:1803.02320 [INSPIRE].
H. Itoyama, T. Oota and K. Yano, Discrete Painleve system and the double scaling limit of the matrix model for irregular conformal block and gauge theory, arXiv:1805.05057 [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].
K. Mashimo, Weyl group of exceptional root system (in Japanese), Yuzawa, Japan, (2013).
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Kubo, N., Moriyama, S. & Nosaka, T. Symmetry breaking in quantum curves and super Chern-Simons matrix models. J. High Energ. Phys. 2019, 210 (2019). https://doi.org/10.1007/JHEP01(2019)210
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DOI: https://doi.org/10.1007/JHEP01(2019)210