Multimatrix models and tri-Sasaki Einstein spaces
Multimatrix models and tri-Sasaki Einstein spaces
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多重矩阵模型和三佐佐木爱因斯坦空间
DOI：
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发表时间：
2010
期刊：
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通讯作者：
Tiberiu Teşileanu
中科院分区：
文献类型：
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作者：
C. Herzog;I. Klebanov;S. Pufu;Tiberiu Teşileanu
定域化方法将S{sup 3}上N{>=}2超对称Chern-Simons规范理论中的路径积分约化为多矩阵积分。最近对N=6超共形U（N）xU（N）Aharony-Bergman-Jafferis-Maldacena理论的这种双矩阵积分的评估与AdS/CFT对应产生了详细的一致性，特别是解释了自由能的N{sup 3/2}标度。研究了一类描述N=3超共形U（N）{supp} Chern-Simons规范理论的p-矩阵积分.我们提出了一个简单的方法，使我们能够评估的本征值密度和自由能在大N限制保持陈-西蒙斯水平k{sub i}固定。对偶M-理论背景是AdS{sub 4}xY，其中Y是由k{sub i}指定的7维三维Sasaki Einstein空间。重力自由能与Y的体积的平方根成反比。我们找到了p-矩阵自由能的一般公式，它与三-Sasaki爱因斯坦空间Y的体积的现有结果一致，从而提供了相应的AdS{sub 4}/CFT{sub 3}对偶性的彻底测试。这个公式与Chern-Simons规范理论的Seiberg对偶是一致的。
Localization methods reduce the path integrals in N{>=}2 supersymmetric Chern-Simons gauge theories on S{sup 3} to multimatrix integrals. A recent evaluation of such a two-matrix integral for the N=6 superconformal U(N)xU(N) Aharony-Bergman-Jafferis-Maldacena theory produced detailed agreement with the AdS/CFT correspondence, explaining, in particular, the N{sup 3/2} scaling of the free energy. We study a class of p-matrix integrals describing N=3 superconformal U(N){sup p} Chern-Simons gauge theories. We present a simple method that allows us to evaluate the eigenvalue densities and the free energies in the large N limit keeping the Chern-Simons levels k{sub i} fixed. The dual M-theory backgrounds are AdS{sub 4}xY, where Y are seven-dimensional tri-Sasaki Einstein spaces specified by the k{sub i}. The gravitational free energy scales inversely with the square root of the volume of Y. We find a general formula for the p-matrix free energies that agrees with the available results for volumes of the tri-Sasaki Einstein spaces Y, thus providing a thorough test of the corresponding AdS{sub 4}/CFT{sub 3} dualities. This formula is consistent with the Seiberg duality conjectured for Chern-Simons gauge theories.