Built on

K. Becker, M. Becker ans A. Strominger, “Fivebranes, membranes and non-perturbative string theory,” Nucl. Phys. B 456
1995
Earlier work this paper cites.
J. M. Maldacena, “Wilson loops in large N field theories,” Phys. Rev. Lett. 80
1998
Earlier work this paper cites.
R. Corrado, K. Pilch and N. P. Warner, “An N=2 supersymmetric membrane flow,” Nucl. Phys. B 629
2002
Earlier work this paper cites.
E. Lerman, “Contact toric manifolds,” J. Symplectic Geom. 1
2003
Earlier work this paper cites.
O. Lunin and J. M. Maldacena, “Deforming field theories with U(1) x U(1) global symmetry and their gravity duals,” JHEP 0505
2005
Earlier work this paper cites.
A. Butti, D. Forcella and A. Zaffaroni, “The Dual superconformal theory for L p,q|r
2005
Earlier work this paper cites.
D. Martelli, J. Sparks and S. T. Yau, “The geometric dual of a-maximisation for toric Sasaki-Einstein manifolds,” Commun. Math. Phys. 268
2006
Earlier work this paper cites.
S. Franco, A. Hanany, D. Martelli, J. Sparks, D. Vegh and B. Wecht, “Gauge theories from toric geometry and brane tilings,” JHEP 0601
2006
Earlier work this paper cites.
S. Benvenuti and M. Kruczenski, “From Sasaki-Einstein spaces to quivers via BPS geodesics: L p,q|r
2006
Earlier work this paper cites.
O. Aharony, O. Bergman, D. L. Jafferis and J. Maldacena, “ 𝒩 = 6 {\cal N}=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals,” JHEP 0810
Original
2008
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M. Benna, I. Klebanov, T. Klose and M. Smedback, “Superconformal Chern-Simons Theories and AdS(4)/CFT(3) Correspondence,” JHEP 0809
Original
2008
Earlier work this paper cites.
D. Martelli and J. Sparks, “Moduli spaces of Chern-Simons quiver gauge theories and AdS(4)/CFT(3),” Phys. Rev. D 78
Original
2008
Earlier work this paper cites.
D. L. Jafferis and A. Tomasiello, “A Simple class of N=3 gauge/gravity duals,” JHEP 0810
Original
2008
Earlier work this paper cites.
A. Hanany and A. Zaffaroni, “Tilings, Chern-Simons Theories and M2 Branes,” JHEP 0810
Original
2008
Earlier work this paper cites.
K. Ueda and M. Yamazaki, “Toric Calabi-Yau four-folds dual to Chern-Simons-matter theories,” JHEP 0812
Original
2008
Earlier work this paper cites.
S. Franco, A. Hanany, J. Park and D. Rodriguez-Gomez, “Towards M2-brane Theories for Generic Toric Singularities,” JHEP 0812
Original
2008
Earlier work this paper cites.
D. Martelli, J. Sparks and S. T. Yau, “Sasaki-Einstein manifolds and volume minimisation,” Commun. Math. Phys. 280
2008
Earlier work this paper cites.

Similar

A. Hanany, D. Vegh and A. Zaffaroni, “Brane Tilings and M2 Branes,” JHEP 0903
Original
2009
Cited alongside, same era.
S. Franco, I. R. Klebanov and D. Rodriguez-Gomez, “M2-branes on Orbifolds of the Cone over Q**1,1,1,” JHEP 0908
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Cited alongside, same era.
J. Davey, A. Hanany, N. Mekareeya and G. Torri, “Phases of M2-brane Theories,” JHEP 0906
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Cited alongside, same era.
J. Davey, A. Hanany, N. Mekareeya and G. Torri, “Higgsing M2-brane Theories,” JHEP 0911
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Cited alongside, same era.
I. Klebanov, T. Klose and A. Murugan, “AdS(4)/CFT(3) Squashed, Stretched and Warped,” JHEP 0903
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Then

A. Hanany and Y. -H. He, “Chern-Simons: Fano and Calabi-Yau,” Adv. High Energy Phys. 2011
Original
2011
Later among the works it cites.
M. Gabella, D. Martelli, A. Passias and J. Sparks, “The free energy of 𝒩 = 2 {\cal N}=2 supersymmetric AdS 4 solutions of M-theory,” JHEP 1110
2011
Later among the works it cites.
D. Martelli and J. Sparks, “The large N limit of quiver matrix models and Sasaki-Einstein manifolds,” Phys. Rev. D 84
Original
2011
Later among the works it cites.
S. Cheon, H. Kim and N. Kim, “Calculating the partition function of N=2 Gauge theories on S 3 S^{3} and AdS/CFT correspondence,” JHEP 1105
Original
2011
Later among the works it cites.
D. L. Jafferis, I. R. Klebanov, S. S. Pufu and B. R. Safdi, “Towards the F-Theorem: N=2 Field Theories on the Three-Sphere,” JHEP 1106

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2013

Wilson loops and the geometry of matrix models in AdS_4/CFT_3

Farquet, Daniel, Sparks, James

Understand

We study a general class of supersymmetric AdS_4 x Y_7 solutions of M-theory that have large N dual descriptions as N = 2 Chern-Simons-matter theories on S^3.

The Hamiltonian function h_M for the M-theory circle, with respect to a certain contact structure on Y_7, plays an important role in the duality.
We show that an M2-brane wrapping the M-theory circle, giving a fundamental string in AdS_4, is supersymmetric precisely at the critical points of h_M, and moreover the value of this function at the critical point determines the M2-brane action.
Such a configuration determines the holographic dual of a BPS Wilson loop for a Hopf circle in S^3, and leads to an effective method for computing the Wilson loop on both sides of the correspondence in large classes of examples.

Built on

K. Becker, M. Becker ans A. Strominger, “Fivebranes, membranes and non-perturbative string theory,” Nucl. Phys. B 456
1995
Earlier work this paper cites.
J. M. Maldacena, “Wilson loops in large N field theories,” Phys. Rev. Lett. 80
1998
Earlier work this paper cites.
R. Corrado, K. Pilch and N. P. Warner, “An N=2 supersymmetric membrane flow,” Nucl. Phys. B 629
2002
Earlier work this paper cites.
E. Lerman, “Contact toric manifolds,” J. Symplectic Geom. 1
2003
Earlier work this paper cites.
O. Lunin and J. M. Maldacena, “Deforming field theories with U(1) x U(1) global symmetry and their gravity duals,” JHEP 0505
2005
Earlier work this paper cites.
A. Butti, D. Forcella and A. Zaffaroni, “The Dual superconformal theory for L p,q|r
2005
Earlier work this paper cites.
D. Martelli, J. Sparks and S. T. Yau, “The geometric dual of a-maximisation for toric Sasaki-Einstein manifolds,” Commun. Math. Phys. 268
2006
Earlier work this paper cites.
S. Franco, A. Hanany, D. Martelli, J. Sparks, D. Vegh and B. Wecht, “Gauge theories from toric geometry and brane tilings,” JHEP 0601
2006
Earlier work this paper cites.
S. Benvenuti and M. Kruczenski, “From Sasaki-Einstein spaces to quivers via BPS geodesics: L p,q|r
2006
Earlier work this paper cites.
O. Aharony, O. Bergman, D. L. Jafferis and J. Maldacena, “ 𝒩 = 6 {\cal N}=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals,” JHEP 0810
Original
2008
Earlier work this paper cites.
M. Benna, I. Klebanov, T. Klose and M. Smedback, “Superconformal Chern-Simons Theories and AdS(4)/CFT(3) Correspondence,” JHEP 0809
Original
2008
Earlier work this paper cites.
D. Martelli and J. Sparks, “Moduli spaces of Chern-Simons quiver gauge theories and AdS(4)/CFT(3),” Phys. Rev. D 78
Original
2008
Earlier work this paper cites.
D. L. Jafferis and A. Tomasiello, “A Simple class of N=3 gauge/gravity duals,” JHEP 0810
Original
2008
Earlier work this paper cites.
A. Hanany and A. Zaffaroni, “Tilings, Chern-Simons Theories and M2 Branes,” JHEP 0810
Original
2008
Earlier work this paper cites.
K. Ueda and M. Yamazaki, “Toric Calabi-Yau four-folds dual to Chern-Simons-matter theories,” JHEP 0812
Original
2008
Earlier work this paper cites.
S. Franco, A. Hanany, J. Park and D. Rodriguez-Gomez, “Towards M2-brane Theories for Generic Toric Singularities,” JHEP 0812
Original
2008
Earlier work this paper cites.
D. Martelli, J. Sparks and S. T. Yau, “Sasaki-Einstein manifolds and volume minimisation,” Commun. Math. Phys. 280
2008
Earlier work this paper cites.