Abstract
The AdS/CFT correspondence enables us to probe M-theory on various backgrounds from the corresponding dual gauge theories. Here we investigate in detail a three-dimensional \( U(N)\mathcal{N}=4 \) super Yang-Mills theory coupled to one adjoint hypermultiplet and N f fundamental hypermultiplets, which is large N dual to M-theory on \( Ad{S}_4\times {S}^7/{\mathrm{\mathbb{Z}}}_{N_f} \). Using the localization and the Fermi-gas formulation, we explore non-perturbative corrections to the partition function. As in the ABJM theory, we find that there exists a non-trivial pole cancellation mechanism, which guarantees the theory to be well-defined, between worldsheet instantons and membrane instantons for all rational (in particular, physical or integral) values of N f .
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References
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [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].
N. Seiberg, IR dynamics on branes and space-time geometry, Phys. Lett. B 384 (1996) 81 [hep-th/9606017] [INSPIRE].
N. Seiberg and E. Witten, Gauge dynamics and compactification to three-dimensions, hep-th/9607163 [INSPIRE].
K.A. Intriligator and N. Seiberg, Mirror symmetry in three-dimensional gauge theories, Phys. Lett. B 387 (1996) 513 [hep-th/9607207] [INSPIRE].
J. de Boer, K. Hori, H. Ooguri and Y. Oz, Mirror symmetry in three-dimensional gauge theories, quivers and D-branes, Nucl. Phys. B 493 (1997) 101 [hep-th/9611063] [INSPIRE].
F. Benini, C. Closset and S. Cremonesi, Chiral flavors and M2-branes at toric CY4 singularities, JHEP 02 (2010) 036 [arXiv:0911.4127] [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].
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].
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].
M. Mariño and P. Putrov, ABJM theory as a Fermi gas, J. Stat. Mech. 1203 (2012) P03001 [arXiv:1110.4066] [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].
J. Kallen and M. Mariño, Instanton effects and quantum spectral curves, arXiv:1308.6485 [INSPIRE].
N.A. Nekrasov and S.L. Shatashvili, Quantization of integrable systems and four dimensional gauge theories, arXiv:0908.4052 [INSPIRE].
O. Aharony, O. Bergman and D.L. Jafferis, Fractional M2-branes, JHEP 11 (2008) 043 [arXiv:0807.4924] [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].
J. Kallen, The spectral problem of the ABJ Fermi gas, arXiv:1407.0625 [INSPIRE].
H. Awata, S. Hirano and M. Shigemori, The partition function of ABJ theory, Prog. Theor. Exp. Phys. (2013) 053B04 [arXiv:1212.2966] [INSPIRE].
M. Honda, Direct derivation of “mirror” ABJ partition function, JHEP 12 (2013) 046 [arXiv:1310.3126] [INSPIRE].
A. Grassi and M. Mariño, M-theoretic matrix models, arXiv:1403.4276 [INSPIRE].
M. Mezei and S.S. Pufu, Three-sphere free energy for classical gauge groups, JHEP 02 (2014) 037 [arXiv:1312.0920] [INSPIRE].
A. Kapustin, B. Willett and I. Yaakov, Nonperturbative tests of three-dimensional dualities, JHEP 10 (2010) 013 [arXiv:1003.5694] [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].
K. Okuyama, A note on the partition function of ABJM theory on S 3, Prog. Theor. Phys. 127 (2012) 229 [arXiv:1110.3555] [INSPIRE].
A.B. Zamolodchikov, Painleve III and 2D polymers, Nucl. Phys. B 432 (1994) 427 [hep-th/9409108] [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].
N. Drukker, M. Mariño and P. Putrov, Nonperturbative aspects of ABJM theory, JHEP 11 (2011) 141 [arXiv:1103.4844] [INSPIRE].
A. Grassi, M. Mariño and S. Zakany, Resumming the string perturbation series, arXiv:1405.4214 [INSPIRE].
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].
M. Honda and S. Moriyama, Instanton effects in orbifold ABJM theory, JHEP 08 (2014) 091 [arXiv:1404.0676] [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].
A. Klemm, M. Mariño, M. Schiereck and M. Soroush, ABJM Wilson loops in the Fermi gas approach, arXiv:1207.0611 [INSPIRE].
Y. Hatsuda, M. Honda, S. Moriyama and K. Okuyama, ABJM Wilson loops in arbitrary representations, JHEP 10 (2013) 168 [arXiv:1306.4297] [INSPIRE].
S. Hirano, K. Nii and M. Shigemori, ABJ Wilson loops and Seiberg duality, arXiv:1406.4141 [INSPIRE].
L. Anderson and K. Zarembo, Quantum phase transitions in mass-deformed ABJM matrix model, JHEP 09 (2014) 021 [arXiv:1406.3366] [INSPIRE].
C. Beasley and E. Witten, New instanton effects in string theory, JHEP 02 (2006) 060 [hep-th/0512039] [INSPIRE].
M.-x. Huang and X.-f. Wang, Topological strings and quantum spectral problems, JHEP 09 (2014) 150 [arXiv:1406.6178] [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].
A. Dabholkar, N. Drukker and J. Gomes, Localization in supergravity and quantum AdS 4 /CFT 3 holography, arXiv:1406.0505 [INSPIRE].
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Hatsuda, Y., Okuyama, K. Probing non-perturbative effects in M-theory. J. High Energ. Phys. 2014, 158 (2014). https://doi.org/10.1007/JHEP10(2014)158
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DOI: https://doi.org/10.1007/JHEP10(2014)158