Built on

I. Bars, “Supergroups And Their Representations,” Lectures Appl. Math. 21
1983
Earlier work this paper cites.
K. Becker, M. Becker and A. Strominger, “Five-branes, membranes and nonperturbative string theory,” Nucl. Phys. B 456
1995
Earlier work this paper cites.
H. Ooguri and C. Vafa, “Knot invariants and topological strings,” Nucl. Phys. B 577
2000
Earlier work this paper cites.
J. M. F. Labastida, M. Marino and C. Vafa, “Knots, links and branes at large N,” JHEP 0011
2000
Earlier work this paper cites.
M. Marino and C. Vafa, “Framed knots at large N,” Contemp. Math. 310
2002
Earlier work this paper cites.
M. Aganagic, A. Klemm and C. Vafa, “Disk instantons, mirror symmetry and the duality web,” Z. Naturforsch. A 57
2002
Earlier work this paper cites.
M. Marino and C. Vafa, “Framed knots at large N,” Contemp. Math. 310
2002
Earlier work this paper cites.
E. M. Moens, J. Van der Jeugt, “A determinantal formula for supersymmetric Schur polynomials,” Journal of Algebraic Combinatorics 17.3
2003
Earlier work this paper cites.
R. Dijkgraaf and C. Vafa, “N=1 supersymmetry, deconstruction, and bosonic gauge theories,” hep-th/0302011, R. Dijkgraaf, S. Gukov, V. A. Kazakov and C. Vafa, “Perturbative analysis of gauged matrix models,” Phys. Rev. D 68
2003
Earlier work this paper cites.
M. Aganagic, A. Klemm, M. Marino and C. Vafa, “Matrix model as a mirror of Chern-Simons theory,” JHEP 0402
2004
Earlier work this paper cites.
A. Borodin, G. Olshanski, E. Strahov, “Giambelli compatible point processes,” Advances in Applied Mathematics 37.2
2006
Earlier work this paper cites.
M. Aganagic, R. Dijkgraaf, A. Klemm, M. Marino and C. Vafa, “Topological strings and integrable hierarchies,” Commun. Math. Phys. 261
2006
Earlier work this paper cites.
B. Eynard and N. Orantin, “Invariants of algebraic curves and topological expansion,” Commun. Num. Theor. Phys. 1
2007
Earlier work this paper cites.

Similar

O. Aharony, O. Bergman, D. L. Jafferis and J. Maldacena, “N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals,” JHEP 0810
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2008
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Then

D. L. Jafferis, “The Exact Superconformal R-Symmetry Extremizes Z,” JHEP 1205
Original
2012
Later among the works it cites.
M. Marino and P. Putrov, “ABJM theory as a Fermi gas,” J. Stat. Mech. 1203
Original
2012
Later among the works it cites.
K. Okuyama, “A Note on the Partition Function of ABJM theory on S 3 S^{3} ,” Prog. Theor. Phys. 127
Original
2012
Later among the works it cites.
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 1205
Original
2012
Later among the works it cites.
Y. Hatsuda, S. Moriyama and K. Okuyama, “Exact Results on the ABJM Fermi Gas,” JHEP 1210

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2013

ABJM Wilson Loops in Arbitrary Representations

Hatsuda, Yasuyuki, Honda, Masazumi, Moriyama, Sanefumi et al.

Understand

We study vacuum expectation values (VEVs) of circular half BPS Wilson loops in arbitrary representations in ABJM theory.

We find that those in hook representations are reduced to elementary integrations thanks to the Fermi gas formalism, which are accessible from the numerical studies similar to the partition function in the previous studies.
For non-hook representations, we show that the VEVs in the grand canonical formalism can be exactly expressed as determinants of those in the hook representations.
Using these facts, we can study the instanton effects of the VEVs in various representations.

Built on

I. Bars, “Supergroups And Their Representations,” Lectures Appl. Math. 21
1983
Earlier work this paper cites.
K. Becker, M. Becker and A. Strominger, “Five-branes, membranes and nonperturbative string theory,” Nucl. Phys. B 456
1995
Earlier work this paper cites.
H. Ooguri and C. Vafa, “Knot invariants and topological strings,” Nucl. Phys. B 577
2000
Earlier work this paper cites.
J. M. F. Labastida, M. Marino and C. Vafa, “Knots, links and branes at large N,” JHEP 0011
2000
Earlier work this paper cites.
M. Marino and C. Vafa, “Framed knots at large N,” Contemp. Math. 310
2002
Earlier work this paper cites.
M. Aganagic, A. Klemm and C. Vafa, “Disk instantons, mirror symmetry and the duality web,” Z. Naturforsch. A 57
2002
Earlier work this paper cites.
M. Marino and C. Vafa, “Framed knots at large N,” Contemp. Math. 310
2002
Earlier work this paper cites.
E. M. Moens, J. Van der Jeugt, “A determinantal formula for supersymmetric Schur polynomials,” Journal of Algebraic Combinatorics 17.3
2003
Earlier work this paper cites.
R. Dijkgraaf and C. Vafa, “N=1 supersymmetry, deconstruction, and bosonic gauge theories,” hep-th/0302011, R. Dijkgraaf, S. Gukov, V. A. Kazakov and C. Vafa, “Perturbative analysis of gauged matrix models,” Phys. Rev. D 68
2003
Earlier work this paper cites.
M. Aganagic, A. Klemm, M. Marino and C. Vafa, “Matrix model as a mirror of Chern-Simons theory,” JHEP 0402
2004
Earlier work this paper cites.
A. Borodin, G. Olshanski, E. Strahov, “Giambelli compatible point processes,” Advances in Applied Mathematics 37.2
2006
Earlier work this paper cites.
M. Aganagic, R. Dijkgraaf, A. Klemm, M. Marino and C. Vafa, “Topological strings and integrable hierarchies,” Commun. Math. Phys. 261
2006
Earlier work this paper cites.
B. Eynard and N. Orantin, “Invariants of algebraic curves and topological expansion,” Commun. Num. Theor. Phys. 1
2007
Earlier work this paper cites.