Built on

E. Witten, “Baryons in the 1 / N 1/N Expansion,” Nucl. Phys. B 160
1979
Earlier work this paper cites.
E. H. Lieb, “Thomas–Fermi and related theories of atoms and molecules,” Rev. Mod. Phys. 53
1982
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1984
Earlier work this paper cites.
Y. Tomishima, “The Thomas-Fermi Theory at Finite Temperature Including Weizscker and Correlation Corrections: Temperature Green’s Function Formalism,” J. Phys. Soc. Jpn. 54
1985
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J. Negele and H. Orland, Quantum many-particle systems
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R. Lawrence and L. Rozansky, “Witten-Reshetikhin-Turaev invariants of Seifert manifolds,” Comm. Math. Phys. 205
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M. Mariño, “Chern-Simons theory, matrix integrals, and perturbative three manifold invariants,” Commun. Math. Phys. 253
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O. Aharony, O. Bergman, D. L. Jafferis and J. Maldacena, “N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals,” JHEP 0810
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2008
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2012

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

Marino, Marcos, Putrov, Pavel

Understand

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.

Built on

E. Witten, “Baryons in the 1 / N 1/N Expansion,” Nucl. Phys. B 160
1979
Earlier work this paper cites.
E. H. Lieb, “Thomas–Fermi and related theories of atoms and molecules,” Rev. Mod. Phys. 53
1982
Earlier work this paper cites.
M. Hillery, R. F. O’Connell, M. O. Scully, E. P. Wigner, “Distribution functions in physics: Fundamentals,” Phys. Rept. 106
1984
Earlier work this paper cites.
Y. Tomishima, “The Thomas-Fermi Theory at Finite Temperature Including Weizscker and Correlation Corrections: Temperature Green’s Function Formalism,” J. Phys. Soc. Jpn. 54
1985
Earlier work this paper cites.
J. Negele and H. Orland, Quantum many-particle systems
1998
Earlier work this paper cites.
R. Lawrence and L. Rozansky, “Witten-Reshetikhin-Turaev invariants of Seifert manifolds,” Comm. Math. Phys. 205
1999
Earlier work this paper cites.
M. Mariño, “Chern-Simons theory, matrix integrals, and perturbative three manifold invariants,” Commun. Math. Phys. 253
2004
Earlier work this paper cites.
C. K. Zachos, D. B. Fairlie and T. L. Curtright (eds.), Quantum Mechanics in phase space
2005
Earlier work this paper cites.
D. Gaiotto and X. Yin, “Notes on superconformal Chern-Simons-Matter theories,” JHEP 0708
Original
2007
Earlier work this paper cites.
O. Aharony, O. Bergman, D. L. Jafferis and J. Maldacena, “N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals,” JHEP 0810
Original
2008
Earlier work this paper cites.
Y. Imamura, K. Kimura, “On the moduli space of elliptic Maxwell-Chern-Simons theories,” Prog. Theor. Phys. 120
Original
2008
Earlier work this paper cites.
D. L. Jafferis, A. Tomasiello, “A Simple class of N=3 gauge/gravity duals,” JHEP 0810
Original
2008
Earlier work this paper cites.