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The large N limit of M2-branes on Lens spaces · Around

2012

The large N limit of M2-branes on Lens spaces

Alday, Luis F., Fluder, Martin, Sparks, James

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We study the matrix model for N M2-branes wrapping a Lens space L(p,1) = S^3/Z_p.

This arises from localization of the partition function of the ABJM theory, and has some novel features compared with the case of a three-sphere, including a sum over flat connections and a potential that depends non-trivially on p.
We study the matrix model both numerically and analytically in the large N limit, finding that a certain family of p flat connections give an equal dominant contribution.
At large N we find the same eigenvalue distribution for all p, and show that the free energy is simply 1/p times the free energy on a three-sphere, in agreement with gravity dual expectations.

Built on

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.
A. Kapustin, B. Willett and I. Yaakov, “Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter,” JHEP 1003
Original
2010
Earlier work this paper cites.
N. Hama, K. Hosomichi and S. Lee, “SUSY Gauge Theories on Squashed Three-Spheres,” JHEP 1105
Original
2011
Earlier work this paper cites.

Similar

J. Kallen, “Cohomological localization of Chern-Simons theory,” JHEP 1108
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C. P. Herzog, I. R. Klebanov, S. S. Pufu and T. Tesileanu, “Multi-Matrix Models and Tri-Sasaki Einstein Spaces,” Phys. Rev. D 83
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N. Hama, K. Hosomichi and S. Lee, “Notes on SUSY Gauge Theories on Three-Sphere,” JHEP 1103
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V. Pestun, “Localization of gauge theory on a four-sphere and supersymmetric Wilson loops,” arXiv:0712.2824 [hep-th]
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Y. Imamura and D. Yokoyama, “ 𝒩 = 2 {\cal N}=2 supersymmetric theories on squashed three-sphere,” arXiv:1109.4734 [hep-th]
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D. Gang, “Chern-Simons theory on L(p,q) lens spaces and Localization,” arXiv: 0912.4664 [hep-th]
Cited in the paper.
F. Benini, T. Nishioka and M. Yamazaki, “4d Index to 3d Index and 2d TQFT,” arXiv:1109.0283 [hep-th]
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D. L. Jafferis, “The Exact Superconformal R-Symmetry Extremizes Z,” arXiv: 1012.3210 [hep-th]
Cited in the paper.
D. Martelli and J. Sparks, “The nuts and bolts of supersymmetric gauge theories on biaxially squashed three-spheres,” arXiv:1111.6930 [hep-th]
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Cited in the paper.

Then

N. Drukker, M. Marino and P. Putrov, “From weak to strong coupling in ABJM theory,” Commun. Math. Phys. 306
Original
2011
Later among the works it cites.
M. Marino and P. Putrov, “ABJM theory as a Fermi gas,” J. Stat. Mech. 1203
Original
2012
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