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From necklace quivers to the F -theorem, operator counting, and T (U(N))

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Abstract

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 \( \mathcal{N} = {3} \) 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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Authors and Affiliations

  1. Joseph Henry Laboratories, Princeton University, Princeton, NJ, 08544, USA

    Daniel R. Gulotta, Christopher P. Herzog & Silviu S. Pufu

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  1. Daniel R. Gulotta
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  2. Christopher P. Herzog
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  3. Silviu S. Pufu
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Correspondence to Silviu S. Pufu.

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ArXiv ePrint: 1105.2817

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Gulotta, D.R., Herzog, C.P. & Pufu, S.S. From necklace quivers to the F -theorem, operator counting, and T (U(N)). J. High Energ. Phys. 2011, 77 (2011). https://doi.org/10.1007/JHEP12(2011)077

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