Built on

E. Witten, “Topological Quantum Field Theory,” Commun. Math. Phys. 117
1988
Earlier work this paper cites.
E. Witten, “Quantum Field Theory and the Jones Polynomial,” Commun. Math. Phys. 121
1989
Earlier work this paper cites.
N. Seiberg, “Electric - magnetic duality in supersymmetric nonAbelian gauge theories,” Nucl. Phys. B 435
1995
Earlier work this paper cites.
M. Nishizawa, “On a q-Analogue of the Multiple Gamma Functions,” Lett. Math. Phys. 37
1996
Earlier work this paper cites.
A. Hanany and E. Witten, “Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics,” Nucl. Phys. B 492
1997
Earlier work this paper cites.
A. Giveon and D. Kutasov, “Brane dynamics and gauge theory,” Rev. Mod. Phys. 71
1999
Earlier work this paper cites.
T. Kitao, K. Ohta and N. Ohta, “Three-dimensional gauge dynamics from brane configurations with (p,q) - five-brane,” Nucl. Phys. B 539
1999
Earlier work this paper cites.
M. Marino, “Chern-Simons theory, matrix integrals, and perturbative three manifold invariants,” Commun. Math. Phys. 253
2004
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M. Aganagic, A. Klemm, M. Marino and C. Vafa, “Matrix model as a mirror of Chern-Simons theory,” JHEP 0402
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O. Aharony, O. Bergman and D. L. Jafferis, “Fractional M2-branes,” JHEP 0811
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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
Original
2008
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N. Drukker, J. Plefka and D. Young, “Wilson loops in 3-dimensional N=6 supersymmetric Chern-Simons Theory and their string theory duals,” JHEP 0811
Original
2008
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D. Berenstein and D. Trancanelli, “Three-dimensional N=6 SCFT’s and their membrane dynamics,” Phys. Rev. D 78
Original
2008
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A. Giveon and D. Kutasov, “Seiberg Duality in Chern-Simons Theory,” Nucl. Phys. B 812
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2009
Earlier work this paper cites.
A. Hanany, D. Vegh and A. Zaffaroni, “Brane Tilings and M2 Branes,” JHEP 0903
Original
2009
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A. Armoni, A. Giveon, D. Israel and V. Niarchos, “Brane Dynamics and 3D Seiberg Duality on the Domain Walls of 4D N=1 SYM,” JHEP 0907
Original
2009
Earlier work this paper cites.

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2014

ABJ Wilson loops and Seiberg Duality

Hirano, Shinji, Nii, Keita, Shigemori, Masaki

Understand

We study supersymmetric Wilson loops in the ${\cal N} = 6$ supersymmetric $U(N_1)_k\times U(N_2)_{-k}$ Chern-Simons-matter (CSM) theory, the ABJ theory, at finite $N_1$, $N_2$ and $k$.

This generalizes our previous study on the ABJ partition function.
First computing the Wilson loops in the $U(N_1) \times U(N_2)$ lens space matrix model exactly, we perform an analytic continuation, $N_2$ to $-N_2$, to obtain the Wilson loops in the ABJ theory that is given in terms of a formal series and only valid in perturbation theory.
Via a Sommerfeld-Watson type transform, we provide a nonperturbative completion that renders the formal series well-defined at all couplings.

Built on

E. Witten, “Topological Quantum Field Theory,” Commun. Math. Phys. 117
1988
Earlier work this paper cites.
E. Witten, “Quantum Field Theory and the Jones Polynomial,” Commun. Math. Phys. 121
1989
Earlier work this paper cites.
N. Seiberg, “Electric - magnetic duality in supersymmetric nonAbelian gauge theories,” Nucl. Phys. B 435
1995
Earlier work this paper cites.
M. Nishizawa, “On a q-Analogue of the Multiple Gamma Functions,” Lett. Math. Phys. 37
1996
Earlier work this paper cites.
A. Hanany and E. Witten, “Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics,” Nucl. Phys. B 492
1997
Earlier work this paper cites.
A. Giveon and D. Kutasov, “Brane dynamics and gauge theory,” Rev. Mod. Phys. 71
1999
Earlier work this paper cites.
T. Kitao, K. Ohta and N. Ohta, “Three-dimensional gauge dynamics from brane configurations with (p,q) - five-brane,” Nucl. Phys. B 539
1999
Earlier work this paper cites.
M. Marino, “Chern-Simons theory, matrix integrals, and perturbative three manifold invariants,” Commun. Math. Phys. 253
2004
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.
O. Aharony, O. Bergman and D. L. Jafferis, “Fractional M2-branes,” JHEP 0811
Original
2008
Earlier work this paper cites.
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
Original
2008
Earlier work this paper cites.
N. Drukker, J. Plefka and D. Young, “Wilson loops in 3-dimensional N=6 supersymmetric Chern-Simons Theory and their string theory duals,” JHEP 0811
Original
2008
Earlier work this paper cites.
D. Berenstein and D. Trancanelli, “Three-dimensional N=6 SCFT’s and their membrane dynamics,” Phys. Rev. D 78
Original
2008
Earlier work this paper cites.
A. Giveon and D. Kutasov, “Seiberg Duality in Chern-Simons Theory,” Nucl. Phys. B 812
Original
2009
Earlier work this paper cites.
A. Hanany, D. Vegh and A. Zaffaroni, “Brane Tilings and M2 Branes,” JHEP 0903
Original
2009
Earlier work this paper cites.
A. Armoni, A. Giveon, D. Israel and V. Niarchos, “Brane Dynamics and 3D Seiberg Duality on the Domain Walls of 4D N=1 SYM,” JHEP 0907
Original
2009
Earlier work this paper cites.