TY - JOUR

T1 - Multimatrix models and tri-sasaki Einstein spaces

AU - Herzog, Christopher P.

AU - Klebanov, Igor R.

AU - Pufu, Silviu S.

AU - Tesileanu, Tiberiu

N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2011/2/2

Y1 - 2011/2/2

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevD.83.046001

DO - 10.1103/PhysRevD.83.046001

M3 - Article

AN - SCOPUS:79952227794

VL - 83

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

SN - 1550-7998

IS - 4

M1 - 046001

ER -