Abstract
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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ArXiv ePrint: 1204.1280
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Alday, L.F., Fluder, M. & Sparks, J. The large N limit of M2-branes on Lens spaces. J. High Energ. Phys. 2012, 57 (2012). https://doi.org/10.1007/JHEP10(2012)057
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DOI: https://doi.org/10.1007/JHEP10(2012)057