Multi-Matrix Models and Tri-Sasaki Einstein Spaces

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.

36 pages, 8 figures; v2 improved section 4, refs added; v3 minor improvements, ref added, PRD version

References in corpus (9)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Fractional M2-branes
• Seiberg Duality in Chern-Simons Theory
• On the moduli space of elliptic Maxwell-Chern-Simons theories
• M2-branes on Orbifolds of the Cone over Q^{1,1,1}
• Unquenched flavor and tropical geometry in strongly coupled Chern-Simons-matter theories
• Phases of M2-brane Theories
• On Large N Solution of Gaiotto-Tomasiello Theory
• AdS/CFT with Tri-Sasakian Manifolds

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