The large N limit of M2-branes on Lens spaces

TL;DR

This paper analyzes the large N limit of M2-branes on Lens spaces using a matrix model derived from ABJM theory, revealing that the free energy scales inversely with p and matches gravity dual predictions.

Contribution

It introduces a novel matrix model for M2-branes on Lens spaces, incorporating flat connections and non-trivial p dependence, and demonstrates the eigenvalue distribution and free energy scaling at large N.

Findings

Eigenvalue distribution is independent of p at large N.

Free energy scales as 1/p times the S^3 free energy.

Results agree with gravity dual predictions.

Abstract

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.