The large N limit of quiver matrix models and Sasaki-Einstein manifolds
Abstract
We study the matrix models that result from localization of the partition functions of N=2 Chern-Simons-matter theories on the three-sphere. A large class of such theories are conjectured to be holographically dual to M-theory on Sasaki-Einstein seven-manifolds. We study the M-theory limit (large N and fixed Chern-Simons levels) of these matrix models for various examples, and show that in this limit the free energy reproduces the expected AdS/CFT result of N^{3/2}/Vol(Y)^{1/2}, where Vol(Y) is the volume of the corresponding Sasaki-Einstein metric. More generally we conjecture a relation between the large N limit of the partition function, interpreted as a function of trial R-charges, and the volumes of Sasakian metrics on links of Calabi-Yau four-fold singularities. We verify this conjecture for a family of U(N)^2 Chern-Simons quivers based on M2 branes at hypersurface singularities, and for a U(N)^3 theory based on M2 branes at a toric singularity.
Keywords
Cite
@article{arxiv.1102.5289,
title = {The large N limit of quiver matrix models and Sasaki-Einstein manifolds},
author = {Dario Martelli and James Sparks},
journal= {arXiv preprint arXiv:1102.5289},
year = {2011}
}
Comments
38 pages, 4 figures; v2: minor changes, typos and factor of 2 in eq. (5.19) fixed, references and 2 figures added; v3: new section 4.5 added; v4: more typos fixed, range of validity of (4.19) clarified