%0 electronic Article
%A Alday, F.
%E Fluder, Martin
%E Sparks, James
%D 2012
%G English
%@ 1029-8479
%T The large N | limit of M2-branes on Lens spaces
%J Journal of High Energy Physics
%V 2012
%N 10
%P 1-23
%U http://dx.doi.org/10.1007/JHEP10(2012)057
%K OriginalPaper
%K Supersymmetric gauge theory
%K Gauge-gravity correspondence
%K Chern-Simons Theories
%K 1/N Expansion
%X 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.