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

Jun, 2012
32 pages
Published in:
  • JHEP 11 (2013) 199
  • Published: 2013
e-Print:

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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.
Note:
  • 29 pages, 4 figures
  • Matrix Models
  • Strong Coupling Expansion
  • 1/N Expansion
  • Supersymmetric gauge theory
  • fermion: interaction
  • force: long-range
  • gas: interaction
  • supersymmetry: 2
  • partition function
  • expansion 1/N