## Abstract

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 k_{i} fixed. The dual M-theory backgrounds are AdS_{4}×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.

Original language | English (US) |
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Article number | 046001 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 83 |

Issue number | 4 |

DOIs | |

State | Published - Feb 2 2011 |

## All Science Journal Classification (ASJC) codes

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