期刊
JOURNAL OF HIGH ENERGY PHYSICS
卷 -, 期 12, 页码 -出版社
SPRINGER
DOI: 10.1007/JHEP12(2011)077
关键词
AdS-CFT Correspondence; Chern-Simons Theories; Strong Coupling Expansion; 1/N Expansion
资金
- NSF [PHY-0756966]
- US NSF [PHY-0844827]
- Princeton University
- Sloan Foundation
- Division Of Physics
- Direct For Mathematical & Physical Scien [844827] Funding Source: National Science Foundation
The matrix model of Kapustin, Willett, and Yaakov is a powerful tool for exploring the properties of strongly interacting superconformal Chern-Simons theories in 2+1 dimensions. In this paper, we use this matrix model to study necklace quiver gauge theories with N = 3 supersymmetry and U(N)(d) gauge groups in the limit of large N. In its simplest application, the matrix model computes the free energy of the gauge theory on S-3. The conjectured F-theorem states that this quantity should decrease under renormalization group flow. We show that for a simple class of such flows, the F-theorem holds for our necklace theories. We also provide a relationship between matrix model eigenvalue distributions and numbers of chiral operators that we conjecture holds more generally. Through the AdS/CFT correspondence, there is therefore a natural dual geometric interpretation of the matrix model saddle point in terms of volumes of 7-d tri-Sasaki Einstein spaces and some of their 5-d submanifolds. As a final bonus, our analysis gives us the partition function of the T(U(N)) theory on S-3.
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