### 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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Published in: Journal of High Energy Physics, Vol. 2012, No. 10 (2012), p. 1-23 ; electronic Article English 1029-8479 A r X iv e P rint:1204.1280 Online-Ressource 10.1007/JHEP10(2012)057 Show QR Code
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• 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.