The large N | limit of M2-branes on Lens spaces

We study the matrix model for N M2-branes wrapping a Lens space$ L\left( {p,1} \right)={S^3}/{{\mathbb{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...

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Bibliographic Details
Published in:Journal of High Energy Physics, Vol. 2012, No. 10 (2012), p. 1-23
Main Author: Alday, F.
Other Involved Persons: Fluder, Martin ; Sparks, James
Format: electronic Article
Language:English
ISSN:1029-8479
Item Description:A r X iv e P rint:1204.1280
Physical Description:Online-Ressource
DOI:10.1007/JHEP10(2012)057
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520 |a We study the matrix model for N M2-branes wrapping a Lens space$ L\left( {p,1} \right)={S^3}/{{\mathbb{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. 
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