Multimatrix models and tri-sasaki Einstein spaces

Christopher P. Herzog, Igor R. Klebanov, Silviu S. Pufu, Tiberiu Tesileanu

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193 Scopus citations


Localization methods reduce the path integrals in N≥2 supersymmetric Chern-Simons gauge theories on S3 to multimatrix integrals. A recent evaluation of such a two-matrix integral for the N=6 superconformal U(N)×U(N) Aharony-Bergman-Jafferis-Maldacena 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 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×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.

Original languageEnglish (US)
Article number046001
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number4
StatePublished - Feb 2 2011

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)


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