%0 Journal Article %1 Herzog2011MultiMatrix %A Herzog, Christopher P. %A Klebanov, Igor R. %A Pufu, Silviu S. %A Tesileanu, Tiberiu %D 2011 %J Physical Review D %K matrix-models, quiver-qm %N 4 %R 10.1103/physrevd.83.046001 %T Multi-Matrix Models and Tri-Sasaki Einstein Spaces %U http://dx.doi.org/10.1103/physrevd.83.046001 %V 83 %X Localization methods reduce the path integrals in N >= 2 supersymmetric Chern-Simons gauge theories on S^3 to multi-matrix integrals. A recent evaluation of such a two-matrix integral for the N=6 superconformal U(N) x U(N) ABJM theory produced detailed agreement with the AdS/CFT correspondence, explaining, in particular the N^3/2 scaling of the free energy. We study a class of p-matrix integrals describing N=3 superconformal U(N)^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\_i fixed. The dual M-theory backgrounds are AdS\_4 x Y, where Y are seven-dimensional tri-Sasaki Einstein spaces specified by the k\_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\_4/CFT\_3 dualities. This formula is consistent with the Seiberg duality conjectured for Chern-Simons gauge theories.

@article{Herzog2011MultiMatrix, abstract = {Localization methods reduce the path integrals in {\cal N} \>= 2 supersymmetric Chern-Simons gauge theories on S^3 to multi-matrix integrals. A recent evaluation of such a two-matrix integral for the {\cal N}=6 superconformal U(N) x U(N) ABJM theory produced detailed agreement with the AdS/CFT correspondence, explaining, in particular the N^{3/2} scaling of the free energy. We study a class of p-matrix integrals describing {\cal N}=3 superconformal U(N)^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\_i fixed. The dual M-theory backgrounds are AdS\_4 x Y, where Y are seven-dimensional tri-Sasaki Einstein spaces specified by the k\_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\_4/CFT\_3 dualities. This formula is consistent with the Seiberg duality conjectured for Chern-Simons gauge theories.}, added-at = {2019-02-26T10:37:35.000+0100}, archiveprefix = {arXiv}, author = {Herzog, Christopher P. and Klebanov, Igor R. and Pufu, Silviu S. and Tesileanu, Tiberiu}, biburl = {https://www.bibsonomy.org/bibtex/2dd8c5a3ec5988ff9295f2f6bbccbb05b/acastro}, citeulike-article-id = {14595441}, citeulike-linkout-0 = {http://arxiv.org/abs/1011.5487}, citeulike-linkout-1 = {http://arxiv.org/pdf/1011.5487}, citeulike-linkout-2 = {http://dx.doi.org/10.1103/physrevd.83.046001}, day = 19, doi = {10.1103/physrevd.83.046001}, eprint = {1011.5487}, interhash = {dd621c286588cbba1c3c691aad1735ea}, intrahash = {dd8c5a3ec5988ff9295f2f6bbccbb05b}, journal = {Physical Review D}, keywords = {matrix-models, quiver-qm}, month = mar, number = 4, posted-at = {2018-05-28 16:30:38}, priority = {2}, timestamp = {2019-02-26T10:37:35.000+0100}, title = {{Multi-Matrix Models and Tri-Sasaki Einstein Spaces}}, url = {http://dx.doi.org/10.1103/physrevd.83.046001}, volume = 83, year = 2011 }