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arXiv · 1206.6346

Interacting fermions and N=2 Chern-Simons-matter theories

Marcos Marino·Pavel Putrov
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Abstract

The partition function on the three-sphere of N=3 Chern-Simons-matter theories can be formulated in terms of an ideal Fermi gas. In this paper we show that, in theories with N=2 supersymmetry, the partition function corresponds to a gas of interacting fermions in one dimension. The large N limit is the thermodynamic limit of the gas and it can be analyzed with the Hartree and Thomas-Fermi approximations, which lead to the known large N solutions of these models. We use this interacting fermion picture to analyze in detail N=2 theories with one single node. In the case of theories with no long-range forces we incorporate exchange effects and argue that the partition function is given by an Airy function, as in N=3 theories. For the theory with g adjoint superfields and long-range forces, the Thomas-Fermi approximation leads to an integral equation which determines the large N, strongly coupled R-charge.

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Marcos Marino, Pavel Putrov. 2012-06-27. Interacting fermions and N=2 Chern-Simons-matter theories. https://doi.org/10.1007/jhep11(2013)199

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