Journal of High Energy Physics

, 2013:199 | Cite as

Interacting fermions and \( \mathcal{N} \) = 2 Chern-Simons-matter theories

  • Marcos Mariño
  • Pavel PutrovEmail author


The partition function on the three-sphere of \( \mathcal{N} \) = 3 Chern-Simons-matter theories can be formulated in terms of an ideal Fermi gas. In this paper we show that, in theories with \( \mathcal{N} \) = 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 \( \mathcal{N} \) = 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 \( \mathcal{N} \) = 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.


Matrix Models Strong Coupling Expansion 1/N Expansion Supersymmetric gauge theory 


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Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  1. 1.Département de Physique Théorique et section de MathématiquesUniversité de GenèveGenèveSwitzerland

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