2010/11/30 by Christopher P. Herzog, Igor R. Klebanov, Silviu S. Pufu +1 · 2 citations
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1103/physrevd.83.046001
published as Phys.Rev.D83:046001,2011 · 36 pages, 8 figures; v2 improved section 4, refs added; v3 minor improvements, ref added, PRD version
arxiv created 2011/03/19 · arxiv updated 2015/03/17
Localization methods reduce the path integrals in \cal N >= 2 supersymmetric Chern-Simons gauge theories on S3 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 N3/2 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 ki fixed. The dual M-theory backgrounds are AdS4 x Y, where Y are seven-dimensional tri-Sasaki Einstein spaces specified by the ki. 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 AdS4/CFT3 dualities. This formula is consistent with the Seiberg duality conjectured for Chern-Simons gauge theories.