The large N limit of quiver matrix models and Sasaki-Einstein manifolds
The large N limit of quiver matrix models and Sasaki-Einstein manifolds
复制标题
箭袋矩阵模型和Sasaki-Einstein流形的大N极限
DOI：
--
复制
发表时间：
2011
期刊：
影响因子：
--
通讯作者：
J. Sparks
中科院分区：
文献类型：
--
作者：
D. Martelli;J. Sparks
我们研究了N=2的Chern-Simons物质理论配分函数在三球面上局部化所产生的矩阵模型。有一大类这样的理论被猜想为佐佐木-爱因斯坦七维流形上的M-理论的全息对偶。我们研究了各种情况下这些矩阵模型的M理论极限(大N和固定的Chern-Simons能级)，并表明在这个极限下，自由能重现了N^{3/2}/Vol(Y)^{1/2}的预期ADS/CFT结果，其中Vol(Y)是相应的Sasaki-Einstein度规的体积。更一般地，我们猜测配分函数的大N极限与Calabi-Yau四重奇点链环上的Sasakian度量的体积之间的关系。我们对基于超曲面奇点的M2膜的U(N)^2 Chern-Simons箭图和基于环奇点的M2膜的U(N)^3理论验证了这一猜想。
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.