Multimatrix models and tri-Sasaki Einstein spaces

Journal Article · Tue Feb 15 04:00:00 EST 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.83.046001· OSTI ID:21505041

Herzog, Christopher P; Pufu, Silviu S; Tesileanu, Tiberiu ^[1]; Klebanov, Igor R ^[1]

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1. Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08544 (United States)

Localization methods reduce the path integrals in N{>=}2 supersymmetric Chern-Simons gauge theories on S{sup 3} to multimatrix integrals. A recent evaluation of such a two-matrix integral for the N=6 superconformal U(N)xU(N) Aharony-Bergman-Jafferis-Maldacena theory produced detailed agreement with the AdS/CFT correspondence, explaining, in particular, the N{sup 3/2} scaling of the free energy. We study a class of p-matrix integrals describing N=3 superconformal U(N){sup 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{sub i} fixed. The dual M-theory backgrounds are AdS{sub 4}xY, where Y are seven-dimensional tri-Sasaki Einstein spaces specified by the k{sub 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{sub 4}/CFT{sub 3} dualities. This formula is consistent with the Seiberg duality conjectured for Chern-Simons gauge theories.

• OSTI ID: 21505041
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 4 Vol. 83; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANTI DE SITTER SPACE
DENSITY
DUALITY
EIGENVALUES
ENERGY
EVALUATION
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FREE ENERGY
GAUGE INVARIANCE
INVARIANCE PRINCIPLES
LIE GROUPS
M-THEORY
MATHEMATICAL SPACE
PHYSICAL PROPERTIES
QUANTUM FIELD THEORY
SCALING
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SUPERSYMMETRY
SYMMETRY
SYMMETRY GROUPS
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U GROUPS