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

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.

29 pages, 4 figures

References in corpus (7)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Notes on SUSY Gauge Theories on Three-Sphere
• Summing Up All Genus Free Energy of ABJM Matrix Model
• Les Houches lectures on matrix models and topological strings
• On the moduli space of elliptic Maxwell-Chern-Simons theories
• ABJM Wilson loops in the Fermi gas approach
• On Large N Solution of Gaiotto-Tomasiello Theory

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