Abstract
We find new bilinear relations for the partition functions of the U(N)k × U(N + M)−k ABJ theory with two parameter mass deformation (m1, m2), which generalize the \(\mathfrak{q}\)-Toda-like equation found previously for m1 = m2. By combining the bilinear relations with the Seiberg-like dualities and the duality cascade relations, we can determine the exact values of the partition functions recursively with respect to N. This method is more efficient than the exact calculation by the standard TBA-like approach in the Fermi gas formalism. As an application we study the large N asymptotics of the partition function with the mass parameters in the supercritical regime where the large N expansion obtained for small mass parameters is invalid.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].
K. Hosomichi et al., N = 4 Superconformal Chern-Simons Theories with Hyper and Twisted Hyper Multiplets, JHEP 07 (2008) 091 [arXiv:0805.3662] [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].
S. Mukhi and C. Papageorgakis, M2 to D2, JHEP 05 (2008) 085 [arXiv:0803.3218] [INSPIRE].
Y. Pang and T. Wang, From N M2’s to N D2’s, Phys. Rev. D 78 (2008) 125007 [arXiv:0807.1444] [INSPIRE].
I. Jeon, N. Lambert and P. Richmond, Periodic Arrays of M2-Branes, JHEP 11 (2012) 100 [arXiv:1206.6699] [INSPIRE].
A. Gustavsson and S.-J. Rey, Enhanced N = 8 Supersymmetry of ABJM Theory on R8 and R8/Z2, arXiv:0906.3568 [INSPIRE].
O.-K. Kwon, P. Oh and J. Sohn, Notes on Supersymmetry Enhancement of ABJM Theory, JHEP 08 (2009) 093 [arXiv:0906.4333] [INSPIRE].
D. Bashkirov and A. Kapustin, Supersymmetry enhancement by monopole operators, JHEP 05 (2011) 015 [arXiv:1007.4861] [INSPIRE].
D. Bashkirov and A. Kapustin, Dualities between N = 8 superconformal field theories in three dimensions, JHEP 05 (2011) 074 [arXiv:1103.3548] [INSPIRE].
K. Jensen and A. Karch, ABJM Mirrors and a Duality of Dualities, JHEP 09 (2009) 004 [arXiv:0906.3013] [INSPIRE].
N. Lambert and C. Papageorgakis, Relating U(N) × U(N) to SU(N) × SU(N) Chern-Simons Membrane theories, JHEP 04 (2010) 104 [arXiv:1001.4779] [INSPIRE].
A. Basu and J.A. Harvey, The M2-M5 brane system and a generalized Nahm’s equation, Nucl. Phys. B 713 (2005) 136 [hep-th/0412310] [INSPIRE].
A. Gustavsson, Selfdual strings and loop space Nahm equations, JHEP 04 (2008) 083 [arXiv:0802.3456] [INSPIRE].
H. Nastase, C. Papageorgakis and S. Ramgoolam, The Fuzzy S2 structure of M2-M5 systems in ABJM membrane theories, JHEP 05 (2009) 123 [arXiv:0903.3966] [INSPIRE].
S. Terashima and F. Yagi, M5-brane Solution in ABJM Theory and Three-algebra, JHEP 12 (2009) 059 [arXiv:0909.3101] [INSPIRE].
N. Lambert and C. Papageorgakis, Nonabelian (2, 0) Tensor Multiplets and 3-algebras, JHEP 08 (2010) 083 [arXiv:1007.2982] [INSPIRE].
T. Nosaka and S. Terashima, M5-branes in ABJM theory and Nahm equation, Phys. Rev. D 86 (2012) 125027 [arXiv:1208.1108] [INSPIRE].
K. Sakai and S. Terashima, Integrability of BPS equations in ABJM theory, JHEP 11 (2013) 002 [arXiv:1308.3583] [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, Nonperturbative Tests of Three-Dimensional Dualities, JHEP 10 (2010) 013 [arXiv:1003.5694] [INSPIRE].
D.L. Jafferis, The Exact Superconformal R-Symmetry Extremizes Z, JHEP 05 (2012) 159 [arXiv:1012.3210] [INSPIRE].
N. Hama, K. Hosomichi and S. Lee, Notes on SUSY Gauge Theories on Three-Sphere, JHEP 03 (2011) 127 [arXiv:1012.3512] [INSPIRE].
N. Hama, K. Hosomichi and S. Lee, SUSY Gauge Theories on Squashed Three-Spheres, JHEP 05 (2011) 014 [arXiv:1102.4716] [INSPIRE].
I.R. Klebanov and A.A. Tseytlin, Near extremal black hole entropy and fluctuating three-branes, Nucl. Phys. B 479 (1996) 319 [hep-th/9607107] [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].
R.C. Santamaria, M. Mariño and P. Putrov, Unquenched flavor and tropical geometry in strongly coupled Chern-Simons-matter theories, JHEP 10 (2011) 139 [arXiv:1011.6281] [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 et al., Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant, JHEP 05 (2012) 121 [arXiv:1202.5300] [INSPIRE].
M. Honda et al., Monte Carlo studies of 3d N = 6 SCFT via localization method, PoS LATTICE2012 (2012) 233 [arXiv:1211.6844] [INSPIRE].
A. Amariti, C. Klare and M. Siani, The Large N Limit of Toric Chern-Simons Matter Theories and Their Duals, JHEP 10 (2012) 019 [arXiv:1111.1723] [INSPIRE].
D. Gang, C. Hwang, S. Kim and J. Park, Tests of AdS4/CFT3 correspondence for \(\mathcal{N}\) = 2 chiral-like theory, JHEP 02 (2012) 079 [arXiv:1111.4529] [INSPIRE].
D. Martelli and J. Sparks, The large N limit of quiver matrix models and Sasaki-Einstein manifolds, Phys. Rev. D 84 (2011) 046008 [arXiv:1102.5289] [INSPIRE].
S. Cheon, H. Kim and N. Kim, Calculating the partition function of N = 2 Gauge theories on S3 and AdS/CFT correspondence, JHEP 05 (2011) 134 [arXiv:1102.5565] [INSPIRE].
A. Amariti and S. Franco, Free Energy vs Sasaki-Einstein Volume for Infinite Families of M2-Brane Theories, JHEP 09 (2012) 034 [arXiv:1204.6040] [INSPIRE].
J.T. Liu and X. Zhang, The large-N partition function for non-parity-invariant Chern-Simons-matter theories, JHEP 12 (2020) 007 [arXiv:2008.09642] [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].
P.M. Crichigno, C.P. Herzog and D. Jain, Free Energy of \({\widehat{D}}_{n}\) Quiver Chern-Simons Theories, JHEP 03 (2013) 039 [arXiv:1211.1388] [INSPIRE].
A. Amariti, M. Fazzi, N. Mekareeya and A. Nedelin, New 3d \(\mathcal{N}\) = 2 SCFT’s with N3/2 scaling, JHEP 12 (2019) 111 [arXiv:1903.02586] [INSPIRE].
D.R. Gulotta, C.P. Herzog and T. Nishioka, The ABCDEF’s of Matrix Models for Supersymmetric Chern-Simons Theories, JHEP 04 (2012) 138 [arXiv:1201.6360] [INSPIRE].
D.L. Jafferis, I.R. Klebanov, S.S. Pufu and B.R. Safdi, Towards the F-Theorem: N = 2 Field Theories on the Three-Sphere, JHEP 06 (2011) 102 [arXiv:1103.1181] [INSPIRE].
D. Jain, Deconstructing Deformed D-quivers, arXiv:1512.08955 [INSPIRE].
Y. Imamura and D. Yokoyama, N = 2 supersymmetric theories on squashed three-sphere, Phys. Rev. D 85 (2012) 025015 [arXiv:1109.4734] [INSPIRE].
L.F. Alday, M. Fluder and J. Sparks, The large N limit of M2-branes on Lens spaces, JHEP 10 (2012) 057 [arXiv:1204.1280] [INSPIRE].
M. Mariño and P. Putrov, Interacting fermions and N = 2 Chern-Simons-matter theories, JHEP 11 (2013) 199 [arXiv:1206.6346] [INSPIRE].
Y. Hatsuda, ABJM on ellipsoid and topological strings, JHEP 07 (2016) 026 [arXiv:1601.02728] [INSPIRE].
M. Mariño and P. Putrov, ABJM theory as a Fermi gas, J. Stat. Mech. 1203 (2012) P03001 [arXiv:1110.4066] [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].
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, S. Moriyama and K. Okuyama, Exact Results on the ABJM Fermi Gas, JHEP 10 (2012) 020 [arXiv:1207.4283] [INSPIRE].
M. Mezei and S.S. Pufu, Three-sphere free energy for classical gauge groups, JHEP 02 (2014) 037 [arXiv:1312.0920] [INSPIRE].
A. Grassi and M. Mariño, M-theoretic matrix models, JHEP 02 (2015) 115 [arXiv:1403.4276] [INSPIRE].
M. Honda and S. Moriyama, Instanton Effects in Orbifold ABJM Theory, JHEP 08 (2014) 091 [arXiv:1404.0676] [INSPIRE].
Y. Hatsuda and K. Okuyama, Probing non-perturbative effects in M-theory, JHEP 10 (2014) 158 [arXiv:1407.3786] [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].
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 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].
S. Bhattacharyya, A. Grassi, M. Mariño and A. Sen, A One-Loop Test of Quantum Supergravity, Class. Quant. Grav. 31 (2014) 015012 [arXiv:1210.6057] [INSPIRE].
J.T. Liu and W. Zhao, One-loop supergravity on AdS4 × S7/ℤk and comparison with ABJM theory, JHEP 11 (2016) 099 [arXiv:1609.02558] [INSPIRE].
N. Bobev et al., A compendium of logarithmic corrections in AdS/CFT, arXiv:2312.08909 [INSPIRE].
M. Beccaria and A.A. Tseytlin, Comments on ABJM free energy on S3 at large N and perturbative expansions in M-theory and string theory, Nucl. Phys. B 994 (2023) 116286 [arXiv:2306.02862] [INSPIRE].
N. Bobev, A.M. Charles, K. Hristov and V. Reys, The Unreasonable Effectiveness of Higher-Derivative Supergravity in AdS4 Holography, Phys. Rev. Lett. 125 (2020) 131601 [arXiv:2006.09390] [INSPIRE].
N. Bobev, A.M. Charles, K. Hristov and V. Reys, Higher-derivative supergravity, AdS4 holography, and black holes, JHEP 08 (2021) 173 [arXiv:2106.04581] [INSPIRE].
K. Hristov and V. Reys, Factorization of log-corrections in AdS4/CFT3 from supergravity localization, JHEP 12 (2021) 031 [arXiv:2107.12398] [INSPIRE].
K. Hristov, 4d \(\mathcal{N}\) = 2 supergravity observables from Nekrasov-like partition functions, JHEP 02 (2022) 079 [arXiv:2111.06903] [INSPIRE].
N. Bobev, J. Hong and V. Reys, Large N Partition Functions, Holography, and Black Holes, Phys. Rev. Lett. 129 (2022) 041602 [arXiv:2203.14981] [INSPIRE].
K. Hristov, ABJM at finite N via 4d supergravity, JHEP 10 (2022) 190 [arXiv:2204.02992] [INSPIRE].
N. Bobev, J. Hong and V. Reys, Large N partition functions of the ABJM theory, JHEP 02 (2023) 020 [arXiv:2210.09318] [INSPIRE].
N. Bobev, J. Hong and V. Reys, Large N partition functions of 3d holographic SCFTs, JHEP 08 (2023) 119 [arXiv:2304.01734] [INSPIRE].
F.F. Gautason, V.G.M. Puletti and J. van Muiden, Quantized strings and instantons in holography, JHEP 08 (2023) 218 [arXiv:2304.12340] [INSPIRE].
M. Beccaria, S. Giombi and A.A. Tseytlin, Instanton contributions to the ABJM free energy from quantum M2 branes, JHEP 10 (2023) 029 [arXiv:2307.14112] [INSPIRE].
A. Dabholkar, N. Drukker and J. Gomes, Localization in supergravity and quantum AdS4/CFT3 holography, JHEP 10 (2014) 090 [arXiv:1406.0505] [INSPIRE].
P. Caputa and S. Hirano, Airy Function and 4d Quantum Gravity, JHEP 06 (2018) 106 [arXiv:1804.00942] [INSPIRE].
N.B. Agmon, S.M. Chester and S.S. Pufu, A new duality between \(\mathcal{N}\) = 8 superconformal field theories in three dimensions, JHEP 06 (2018) 005 [arXiv:1708.07861] [INSPIRE].
N.B. Agmon, S.M. Chester and S.S. Pufu, Solving M-theory with the Conformal Bootstrap, JHEP 06 (2018) 159 [arXiv:1711.07343] [INSPIRE].
S.M. Chester, S.S. Pufu and X. Yin, The M-Theory S-Matrix From ABJM: Beyond 11D Supergravity, JHEP 08 (2018) 115 [arXiv:1804.00949] [INSPIRE].
D.J. Binder, S.M. Chester and S.S. Pufu, Absence of D4R4 in M-Theory From ABJM, JHEP 04 (2020) 052 [arXiv:1808.10554] [INSPIRE].
D.J. Binder, S.M. Chester and S.S. Pufu, AdS4/CFT3 from weak to strong string coupling, JHEP 01 (2020) 034 [arXiv:1906.07195] [INSPIRE].
N.B. Agmon, S.M. Chester and S.S. Pufu, The M-theory Archipelago, JHEP 02 (2020) 010 [arXiv:1907.13222] [INSPIRE].
S.M. Chester, R.R. Kalloor and A. Sharon, 3d \(\mathcal{N}\) = 4 OPE coefficients from Fermi gas, JHEP 07 (2020) 041 [arXiv:2004.13603] [INSPIRE].
D.J. Binder, S.M. Chester, M. Jerdee and S.S. Pufu, The 3d \(\mathcal{N}\) = 6 bootstrap: from higher spins to strings to membranes, JHEP 05 (2021) 083 [arXiv:2011.05728] [INSPIRE].
L.F. Alday, S.M. Chester and H. Raj, ABJM at strong coupling from M-theory, localization, and Lorentzian inversion, JHEP 02 (2022) 005 [arXiv:2107.10274] [INSPIRE].
L.F. Alday, S.M. Chester and H. Raj, M-theory on AdS4 × S7 at 1-loop and beyond, JHEP 11 (2022) 091 [arXiv:2207.11138] [INSPIRE].
S.M. Chester, S.S. Pufu, Y. Wang and X. Yin, Bootstrapping M-theory Orbifolds, arXiv:2312.13112 [INSPIRE].
K. Hosomichi et al., N = 5, 6 Superconformal Chern-Simons Theories and M2-branes on Orbifolds, JHEP 09 (2008) 002 [arXiv:0806.4977] [INSPIRE].
J. Gomis, D. Rodriguez-Gomez, M. Van Raamsdonk and H. Verlinde, A Massive Study of M2-brane Proposals, JHEP 09 (2008) 113 [arXiv:0807.1074] [INSPIRE].
R.C. Myers, Dielectric branes, JHEP 12 (1999) 022 [hep-th/9910053] [INSPIRE].
L. Anderson and K. Zarembo, Quantum Phase Transitions in Mass-Deformed ABJM Matrix Model, JHEP 09 (2014) 021 [arXiv:1406.3366] [INSPIRE].
L. Anderson and J.G. Russo, ABJM Theory with mass and FI deformations and Quantum Phase Transitions, JHEP 05 (2015) 064 [arXiv:1502.06828] [INSPIRE].
T. Nosaka, K. Shimizu and S. Terashima, Large N behavior of mass deformed ABJM theory, JHEP 03 (2016) 063 [arXiv:1512.00249] [INSPIRE].
T. Nosaka, K. Shimizu and S. Terashima, Mass Deformed ABJM Theory on Three Sphere in Large N limit, JHEP 03 (2017) 121 [arXiv:1608.02654] [INSPIRE].
T. Nosaka, Instanton effects in ABJM theory with general R-charge assignments, JHEP 03 (2016) 059 [arXiv:1512.02862] [INSPIRE].
M. Honda, T. Nosaka, K. Shimizu and S. Terashima, Supersymmetry Breaking in a Large N Gauge Theory with Gravity Dual, JHEP 03 (2019) 159 [arXiv:1807.08874] [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].
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].
M. Honda and K. Okuyama, Exact results on ABJ theory and the refined topological string, JHEP 08 (2014) 148 [arXiv:1405.3653] [INSPIRE].
J. Kallen, The spectral problem of the ABJ Fermi gas, JHEP 10 (2015) 029 [arXiv:1407.0625] [INSPIRE].
A. Grassi, Y. Hatsuda and M. Mariño, Topological Strings from Quantum Mechanics, Annales Henri Poincare 17 (2016) 3177 [arXiv:1410.3382] [INSPIRE].
S. Codesido, A. Grassi and M. Mariño, Spectral Theory and Mirror Curves of Higher Genus, Annales Henri Poincare 18 (2017) 559 [arXiv:1507.02096] [INSPIRE].
J. Kallen and M. Mariño, Instanton Effects and Quantum Spectral Curves, Annales Henri Poincare 17 (2016) 1037 [arXiv:1308.6485] [INSPIRE].
M.-X. Huang and X.-F. Wang, Topological Strings and Quantum Spectral Problems, JHEP 09 (2014) 150 [arXiv:1406.6178] [INSPIRE].
X.-F. Wang, X. Wang and M.-X. Huang, A Note on Instanton Effects in ABJM Theory, JHEP 11 (2014) 100 [arXiv:1409.4967] [INSPIRE].
S. Codesido, A. Grassi and M. Mariño, Exact results in \(\mathcal{N}\) = 8 Chern-Simons-matter theories and quantum geometry, JHEP 07 (2015) 011 [arXiv:1409.1799] [INSPIRE].
A. Grassi, Y. Hatsuda and M. Mariño, Quantization conditions and functional equations in ABJ(M) theories, J. Phys. A 49 (2016) 115401 [arXiv:1410.7658] [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].
M. Mariño and S. Zakany, Matrix Models from Operators and Topological Strings, Annales Henri Poincare 17 (2016) 1075 [arXiv:1502.02958] [INSPIRE].
Y. Hatsuda, Spectral zeta function and non-perturbative effects in ABJM Fermi-gas, JHEP 11 (2015) 086 [arXiv:1503.07883] [INSPIRE].
R. Kashaev, M. Mariño and S. Zakany, Matrix Models from Operators and Topological Strings, 2, Annales Henri Poincare 17 (2016) 2741 [arXiv:1505.02243] [INSPIRE].
K. Okuyama and S. Zakany, TBA-like integral equations from quantized mirror curves, JHEP 03 (2016) 101 [arXiv:1512.06904] [INSPIRE].
G. Bonelli, A. Grassi and A. Tanzini, Seiberg-Witten theory as a Fermi gas, Lett. Math. Phys. 107 (2017) 1 [arXiv:1603.01174] [INSPIRE].
A. Grassi, Spectral determinants and quantum theta functions, J. Phys. A 49 (2016) 505401 [arXiv:1604.06786] [INSPIRE].
S. Codesido, J. Gu and M. Mariño, Operators and higher genus mirror curves, JHEP 02 (2017) 092 [arXiv:1609.00708] [INSPIRE].
G. Bonelli, A. Grassi and A. Tanzini, New results in \(\mathcal{N}\) = 2 theories from non-perturbative string, Annales Henri Poincare 19 (2018) 743 [arXiv:1704.01517] [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].
A. Grassi and M. Mariño, The complex side of the TS/ST correspondence, J. Phys. A 52 (2019) 055402 [arXiv:1708.08642] [INSPIRE].
S. Zakany, Quantized mirror curves and resummed WKB, JHEP 05 (2019) 114 [arXiv:1711.01099] [INSPIRE].
S. Codesido, M. Mariño and R. Schiappa, Non-Perturbative Quantum Mechanics from Non-Perturbative Strings, Annales Henri Poincare 20 (2019) 543 [arXiv:1712.02603] [INSPIRE].
A. Grassi and M. Mariño, A Solvable Deformation of Quantum Mechanics, SIGMA 15 (2019) 025 [arXiv:1806.01407] [INSPIRE].
Z. Duan, J. Gu, Y. Hatsuda and T. Sulejmanpasic, Instantons in the Hofstadter butterfly: difference equation, resurgence and quantum mirror curves, JHEP 01 (2019) 079 [arXiv:1806.11092] [INSPIRE].
Y. Emery, M. Mariño and M. Ronzani, Resonances and PT symmetry in quantum curves, JHEP 04 (2020) 150 [arXiv:1902.08606] [INSPIRE].
A. Grassi, J. Gu and M. Mariño, Non-perturbative approaches to the quantum Seiberg-Witten curve, JHEP 07 (2020) 106 [arXiv:1908.07065] [INSPIRE].
G. Bonelli et al., M2-branes and \(\mathfrak{q}\)-Painlevé equations, Lett. Math. Phys. 112 (2022) 109 [arXiv:2202.10654] [INSPIRE].
S.H. Katz, A. Klemm and C. Vafa, Geometric engineering of quantum field theories, Nucl. Phys. B 497 (1997) 173 [hep-th/9609239] [INSPIRE].
N.C. Leung and C. Vafa, Branes and toric geometry, Adv. Theor. Math. Phys. 2 (1998) 91 [hep-th/9711013] [INSPIRE].
R. Gopakumar and C. Vafa, M theory and topological strings. II, hep-th/9812127 [INSPIRE].
T.J. Hollowood, A. Iqbal and C. Vafa, Matrix models, geometric engineering and elliptic genera, JHEP 03 (2008) 069 [hep-th/0310272] [INSPIRE].
H. Nakajima and K. Yoshioka, Instanton counting on blowup. I, Invent. Math. 162 (2005) 313 [math/0306198] [INSPIRE].
H. Nakajima and K. Yoshioka, Lectures on instanton counting, in the proceedings of the CRM Workshop on Algebraic Structures and Moduli Spaces, Montreal, Canada, July 14–20 (2003) [math/0311058] [INSPIRE].
H. Nakajima and K. Yoshioka, Instanton counting on blowup. II. K-theoretic partition function, math/0505553 [INSPIRE].
C.A. Keller and J. Song, Counting Exceptional Instantons, JHEP 07 (2012) 085 [arXiv:1205.4722] [INSPIRE].
A. Grassi and J. Gu, BPS relations from spectral problems and blowup equations, Lett. Math. Phys. 109 (2019) 1271 [arXiv:1609.05914] [INSPIRE].
M. Bershtein and A. Shchechkin, Painlevé equations from Nakajima-Yoshioka blowup relations, Lett. Math. Phys. 109 (2019) 2359 [arXiv:1811.04050] [INSPIRE].
J. Kim et al., Instantons from Blow-up, JHEP 11 (2019) 092 [Erratum ibid. 06 (2020) 124] [arXiv:1908.11276] [INSPIRE].
A. Shchechkin, Blowup relations on ℂ2/ℤ2 from Nakajima-Yoshioka blowup relations, Teor. Mat. Fiz. 206 (2021) 225 [arXiv:2006.08582] [INSPIRE].
T. Nosaka, SU(N) q-Toda equations from mass deformed ABJM theory, JHEP 06 (2021) 060 [arXiv:2012.07211] [INSPIRE].
A. Giveon and D. Kutasov, Seiberg Duality in Chern-Simons Theory, Nucl. Phys. B 812 (2009) 1 [arXiv:0808.0360] [INSPIRE].
B. Assel, Hanany-Witten effect and SL(2, ℤ) dualities in matrix models, JHEP 10 (2014) 117 [arXiv:1406.5194] [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].
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].
C.A. Tracy and H. Widom, Fredholm determinants and the mKdV/Sinh-Gordon hierarchies, Commun. Math. Phys. 179 (1996) 1.
C.A. Tracy and H. Widom, Proofs of two conjectures related to the thermodynamic Bethe ansatz, Commun. Math. Phys. 179 (1996) 667 [solv-int/9509003] [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].
T. Nosaka and S. Yokoyama, Complete factorization in minimal \(\mathcal{N}\) = 4 Chern-Simons-matter theory, JHEP 01 (2018) 001 [arXiv:1706.07234] [INSPIRE].
T. Nosaka and S. Yokoyama, Index and duality of minimal \(\mathcal{N}\) = 4 Chern-Simons-matter theories, JHEP 06 (2018) 028 [arXiv:1804.04639] [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].
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].
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].
S.M. Chester, R.R. Kalloor and A. Sharon, Squashing, Mass, and Holography for 3d Sphere Free Energy, JHEP 04 (2021) 244 [arXiv:2102.05643] [INSPIRE].
M. Bershtein, P. Gavrylenko and A. Marshakov, Cluster Toda chains and Nekrasov functions, Theor. Math. Phys. 198 (2019) 157 [arXiv:1804.10145] [INSPIRE].
Y. Hatsuda and K. Okuyama, Resummations and Non-Perturbative Corrections, JHEP 09 (2015) 051 [arXiv:1505.07460] [INSPIRE].
A. Cagnazzo, D. Sorokin and L. Wulff, String instanton in AdS4 × CP3, JHEP 05 (2010) 009 [arXiv:0911.5228] [INSPIRE].
S. Moriyama and T. Nosaka, 40 bilinear relations of q-Painlevé VI from \(\mathcal{N}\) = 4 super Chern-Simons theory, JHEP 08 (2023) 191 [arXiv:2305.03978] [INSPIRE].
S. Moriyama and T. Nosaka, Affine Symmetries for ABJM Partition Function and its Generalization, arXiv:2312.04206 [INSPIRE].
L. Bao, E. Pomoni, M. Taki and F. Yagi, M5-Branes, Toric Diagrams and Gauge Theory Duality, JHEP 04 (2012) 105 [arXiv:1112.5228] [INSPIRE].
B. Assel, N. Drukker and J. Felix, Partition functions of 3d Dˆ-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].
O. Aharony, S.S. Razamat, N. Seiberg and B. Willett, 3d dualities from 4d dualities, JHEP 07 (2013) 149 [arXiv:1305.3924] [INSPIRE].
A. Amariti, A note on 3D \(\mathcal{N}\) = 2 dualities: real mass flow and partition function, JHEP 03 (2014) 064 [arXiv:1309.6434] [INSPIRE].
K. Shimizu, Aspects of Massive Gauge Theories on Three Sphere in Infinite Mass Limit, JHEP 01 (2019) 090 [arXiv:1809.03679] [INSPIRE].
N. Kubo and K. Nii, 3d \(\mathcal{N}\) = 3 generalized Giveon-Kutasov duality, JHEP 04 (2022) 158 [arXiv:2111.13366] [INSPIRE].
H.-C. Kim and S. Kim, Supersymmetric vacua of mass-deformed M2-brane theory, Nucl. Phys. B 839 (2010) 96 [arXiv:1001.3153] [INSPIRE].
S. Cheon, H.-C. Kim and S. Kim, Holography of mass-deformed M2-branes, arXiv:1101.1101 [INSPIRE].
D. Jang, Y. Kim, O.-K. Kwon and D.D. Tolla, Exact Holography of the Mass-deformed M2-brane Theory, Eur. Phys. J. C 77 (2017) 342 [arXiv:1610.01490] [INSPIRE].
D. Jang, Y. Kim, O.-K. Kwon and D.D. Tolla, Mass-deformed ABJM Theory and LLM Geometries: Exact Holography, JHEP 04 (2017) 104 [arXiv:1612.05066] [INSPIRE].
D. Jang, Y. Kim, O.-K. Kwon and D.D. Tolla, Holography of Massive M2-brane Theory with Discrete Torsion, Eur. Phys. J. C 80 (2020) 224 [arXiv:1906.06881] [INSPIRE].
E. Armanini, L. Griguolo and L. Guerrini, BPS Wilson loops in mass-deformed ABJM theory: Fermi gas expansions and new defect CFT data, arXiv:2401.12288 [INSPIRE].
D.Z. Freedman and S.S. Pufu, The holography of F-maximization, JHEP 03 (2014) 135 [arXiv:1302.7310] [INSPIRE].
N. Kim, Solving Mass-deformed Holography Perturbatively, JHEP 04 (2019) 053 [arXiv:1902.00418] [INSPIRE].
N. Bobev, V.S. Min, K. Pilch and F. Rosso, Mass Deformations of the ABJM Theory: The Holographic Free Energy, JHEP 03 (2019) 130 [arXiv:1812.01026] [INSPIRE].
N. Kim and S.-J. Kim, A perturbative study of holographic mABJM theory, Phys. Lett. B 797 (2019) 134837 [arXiv:1904.09465] [INSPIRE].
L. Anderson and M.M. Roberts, Mass deformed ABJM \(\mathcal{P}\mathcal{T}\) and symmetry, JHEP 04 (2019) 036 [arXiv:1807.10307] [INSPIRE].
D. Gaiotto and T. Okazaki, Sphere correlation functions and Verma modules, JHEP 02 (2020) 133 [arXiv:1911.11126] [INSPIRE].
L. Santilli and M. Tierz, Exact results and Schur expansions in quiver Chern-Simons-matter theories, JHEP 10 (2020) 022 [arXiv:2008.00465] [INSPIRE].
J.G. Russo and G.A. Silva, Exact partition function in U(2) × U(2) ABJM theory deformed by mass and Fayet-Iliopoulos terms, JHEP 12 (2015) 092 [arXiv:1510.02957] [INSPIRE].
Acknowledgments
We are grateful to Mohammad Akhond, Yuhma Asano, Francesco Benini, Friðrik Freyr Gautason, Hirotaka Hayashi, Masazumi Honda, Naotaka Kubo, Sanefumi Moriyama, Jesse van Muiden, Tadashi Okazaki, Valentina Giangreco M. Puletti, Konstantinos C. Rigatos, Minwoo Suh, Huajia Wang and Xinan Zhou for valuable discussions and comments. Preliminary results of this paper were presented in an international conference “KEK theory workshop 2023” held at KEK, Tsukuba, Ibaraki, Japan.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2401.11484
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Nosaka, T. Large N expansion of mass deformed ABJM matrix model: M2-instanton condensation and beyond. J. High Energ. Phys. 2024, 87 (2024). https://doi.org/10.1007/JHEP03(2024)087
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2024)087