Abstract
We study instanton corrections to the vacuum expectation value (VEV) of 1/6 BPS Wilson loops in ABJM theory from the Fermi gas approach. We mainly consider Wilson loops in the fundamental representation and winding Wilson loops, but we also initiate the study of Wilson loops with two boundaries. We find that the membrane instanton corrections to the Wilson loop VEV are determined by the refined topological string in the Nekrasov-Shatashvili limit, and the pole cancellation mechanism between membrane instantons and worldsheet instantons works also in the Wilson loop VEVs as in the case of the partition functions.
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, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [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].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M 2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [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].
I.R. Klebanov and A.A. Tseytlin, Entropy of near extremal black p-branes, Nucl. Phys. B 475 (1996) 164 [hep-th/9604089] [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].
N. Drukker, M. Mariño and P. Putrov, Nonperturbative aspects of ABJM theory, JHEP 11 (2011) 141 [arXiv:1103.4844] [INSPIRE].
M. Mariño and P. Putrov, ABJM theory as a Fermi gas, J. Stat. Mech. 03 (2012) P03001 [arXiv:1110.4066] [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].
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, M. Mariño, S. Moriyama and K. Okuyama, Non-perturbative effects and the refined topological string, JHEP 09 (2014) 168 [arXiv:1306.1734] [INSPIRE].
S. Codesido, A. Grassi and M. Mariño, Exact results in 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].
K. Okuyama, Orientifolding of the ABJ Fermi gas, JHEP 03 (2016) 008 [arXiv:1601.03215] [INSPIRE].
A. Klemm, M. Mariño, M. Schiereck and M. Soroush, Aharony-Bergman-Jafferis-Maldacena Wilson loops in the Fermi gas approach, Z. Naturforsch. A 68 (2013) 178 [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. Matsuno and S. Moriyama, Giambelli identity in super Chern-Simons matrix model, arXiv:1603.04124 [INSPIRE].
Y. Hatsuda and K. Okuyama, Exact results for ABJ Wilson loops and open-closed duality, arXiv:1603.06579 [INSPIRE].
M. Mariño and P. Putrov, Exact results in ABJM theory from topological strings, JHEP 06 (2010) 011 [arXiv:0912.3074] [INSPIRE].
A. Grassi, J. Kallen and M. Mariño, The topological open string wavefunction, Commun. Math. Phys. 338 (2015) 533 [arXiv:1304.6097] [INSPIRE].
M. Mariño and S. Zakany, Exact eigenfunctions and the open topological string, arXiv:1606.05297 [INSPIRE].
J. Kallen and M. Mariño, Instanton effects and quantum spectral curves, Annales Henri Poincaré 17 (2016) 1037 [arXiv:1308.6485] [INSPIRE].
J. Kallen, The spectral problem of the ABJ Fermi gas, JHEP 10 (2015) 029 [arXiv:1407.0625] [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].
X. Wang, G. Zhang and M.-X. Huang, New exact quantization condition for toric Calabi-Yau geometries, Phys. Rev. Lett. 115 (2015) 121601 [arXiv:1505.05360] [INSPIRE].
Y. Hatsuda, Comments on exact quantization conditions and non-perturbative topological strings, arXiv:1507.04799 [INSPIRE].
N. Drukker, J. Plefka and D. Young, Wilson loops in 3-dimensional N = 6 supersymmetric Chern-Simons theory and their string theory duals, JHEP 11 (2008) 019 [arXiv:0809.2787] [INSPIRE].
B. Chen and J.-B. Wu, Supersymmetric Wilson loops in N = 6 super Chern-Simons-matter theory, Nucl. Phys. B 825 (2010) 38 [arXiv:0809.2863] [INSPIRE].
S.-J. Rey, T. Suyama and S. Yamaguchi, Wilson loops in superconformal Chern-Simons theory and fundamental strings in anti-de Sitter supergravity dual, JHEP 03 (2009) 127 [arXiv:0809.3786] [INSPIRE].
N. Drukker and D. Trancanelli, A supermatrix model for N = 6 super Chern-Simons-matter theory, JHEP 02 (2010) 058 [arXiv:0912.3006] [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].
K. Okuyama, A note on the partition function of ABJM theory on S 3, Prog. Theor. Phys. 127 (2012) 229 [arXiv:1110.3555] [INSPIRE].
P. Putrov and M. Yamazaki, Exact ABJM partition function from TBA, Mod. Phys. Lett. A 27 (2012) 1250200 [arXiv:1207.5066] [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 and K. Okuyama, Probing non-perturbative effects in M-theory, JHEP 10 (2014) 158 [arXiv:1407.3786] [INSPIRE].
Y. Hatsuda and K. Okuyama, Resummations and non-perturbative corrections, JHEP 09 (2015) 051 [arXiv:1505.07460] [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].
M. Aganagic, A. Klemm and C. Vafa, Disk instantons, mirror symmetry and the duality web, Z. Naturforsch. A 57 (2002) 1 [hep-th/0105045] [INSPIRE].
Y. Hatsuda, Spectral zeta function and non-perturbative effects in ABJM Fermi-gas, JHEP 11 (2015) 086 [arXiv:1503.07883] [INSPIRE].
S. Hirano, K. Nii and M. Shigemori, ABJ Wilson loops and Seiberg duality, Prog. Theor. Exp. Phys. 2014 (2014) 113B04 [arXiv:1406.4141] [INSPIRE].
S. Matsumoto and S. Moriyama, ABJ fractional brane from ABJM Wilson loop, JHEP 03 (2014) 079 [arXiv:1310.8051] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1607.06157
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Okuyama, K. Instanton corrections of 1/6 BPS Wilson loops in ABJM theory. J. High Energ. Phys. 2016, 125 (2016). https://doi.org/10.1007/JHEP09(2016)125
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2016)125