Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-11-24
Phys.Rev.D83:046001,2011
Physics
High Energy Physics
High Energy Physics - Theory
36 pages, 8 figures; v2 improved section 4, refs added; v3 minor improvements, ref added, PRD version
Scientific paper
10.1103/PhysRevD.83.046001
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.
Herzog Christopher P.
Klebanov Igor R.
Pufu Silviu S.
Teşileanu Tiberiu
No associations
LandOfFree
Multi-Matrix Models and Tri-Sasaki Einstein Spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Multi-Matrix Models and Tri-Sasaki Einstein Spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Multi-Matrix Models and Tri-Sasaki Einstein Spaces will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-586207