Abstract
We study 1/2 BPS Wilson loops in 3d \( \mathcal{N} \) = 4 U(N ) Yang-Mills theory with one adjoint and N f fundamental hypermultiplets from the Fermi gas approach. By numerical fitting, we find the first few worldsheet instanton corrections to the Wilson loops with winding numbers 1, 2 and 3. We verify that our Fermi gas results are consistent with the matrix model results in the planar limit.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M. Mariño and P. Putrov, ABJM theory as a Fermi gas, J. Stat. Mech. 1203 (2012) P03001 [arXiv:1110.4066] [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].
O. Aharony, O. Bergman and D.L. Jafferis, Fractional M 2-branes, JHEP 11 (2008) 043 [arXiv:0807.4924] [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].
Y. Hatsuda, S. Moriyama and K. Okuyama, Exact instanton expansion of the ABJM partition function, PTEP 2015 (2015) 11B104 [arXiv:1507.01678] [INSPIRE].
M. Mariño, Localization at large-N in Chern-Simons-matter theories, arXiv:1608.02959 [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. Matsumoto and S. Moriyama, ABJ fractional brane from ABJM Wilson loop, JHEP 03 (2014) 079 [arXiv:1310.8051] [INSPIRE].
Y. Hatsuda and K. Okuyama, Exact results for ABJ Wilson loops and open-closed duality, JHEP 10 (2016) 132 [arXiv:1603.06579] [INSPIRE].
S. Matsuno and S. Moriyama, Giambelli identity in super Chern-Simons matrix model, arXiv:1603.04124 [INSPIRE].
K. Kiyoshige and S. Moriyama, Dualities in ABJM matrix model from closed string viewpoint, arXiv:1607.06414 [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].
Y. Hatsuda and K. Okuyama, Probing non-perturbative effects in M-theory, JHEP 10 (2014) 158 [arXiv:1407.3786] [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].
Y. Hatsuda, S. Moriyama and K. Okuyama, Instanton effects in ABJM theory from Fermi gas approach, JHEP 01 (2013) 158 [arXiv:1211.1251] [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. 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, Resummations and non-perturbative corrections, JHEP 09 (2015) 051 [arXiv:1505.07460] [INSPIRE].
B. Assel and J. Gomis, Mirror symmetry and loop operators, JHEP 11 (2015) 055 [arXiv:1506.01718] [INSPIRE].
M. Cooke, N. Drukker and D. Trancanelli, A profusion of 1/2 BPS Wilson loops in \( \mathcal{N} \) = 4 Chern-Simons-matter theories, JHEP 10 (2015) 140 [arXiv:1506.07614] [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].
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, Spectral zeta function and non-perturbative effects in ABJM Fermi-gas, JHEP 11 (2015) 086 [arXiv:1503.07883] [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].
K. Okuyama, Probing non-perturbative effects in M-theory on orientifolds, JHEP 01 (2016) 054 [arXiv:1511.02635] [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].
K. Okuyama, Orientifolding of the ABJ Fermi gas, JHEP 03 (2016) 008 [arXiv:1601.03215] [INSPIRE].
K. Okuyama, Instanton corrections of 1/6 BPS Wilson loops in ABJM theory, JHEP 09 (2016) 125 [arXiv:1607.06157] [INSPIRE].
B. Eynard and C. Kristjansen, Exact solution of the O(n) model on a random lattice, Nucl. Phys. B 455 (1995) 577 [hep-th/9506193] [INSPIRE].
B. Eynard and C. Kristjansen, More on the exact solution of the O(n) model on a random lattice and an investigation of the case |n| > 2, Nucl. Phys. B 466 (1996) 463 [hep-th/9512052] [INSPIRE].
T. Suyama, On large-N solution of N = 3 Chern-Simons-adjoint theories, Nucl. Phys. B 867 (2013) 887 [arXiv:1208.2096] [INSPIRE].
G. Borot and B. Eynard, Enumeration of maps with self avoiding loops and the O(n) model on random lattices of all topologies, J. Stat. Mech. 1101 (2011) P01010 [arXiv:0910.5896] [INSPIRE].
Y. Hatsuda, S. Moriyama and K. Okuyama, Instanton bound states in ABJM theory, JHEP 05 (2013) 054 [arXiv:1301.5184] [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].
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. Moriyama and T. Nosaka, Partition functions of superconformal Chern-Simons theories from Fermi gas approach, JHEP 11 (2014) 164 [arXiv:1407.4268] [INSPIRE].
J. Gu, A. Klemm, M. Mariño and J. Reuter, Exact solutions to quantum spectral curves by topological string theory, JHEP 10 (2015) 025 [arXiv:1506.09176] [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: 1610.02116
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. Wilson loops in 3d \( \mathcal{N} \) = 4 SQCD from Fermi gas. J. High Energ. Phys. 2016, 156 (2016). https://doi.org/10.1007/JHEP11(2016)156
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2016)156