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Exact results on the ABJM Fermi gas

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Abstract

We study the Fermi gas quantum mechanics associated to the ABJM matrix model. We develop a method to compute the grand partition function of the ABJM theory, and compute exactly the partition function Z(N) up to N = 9 with the Chern-Simons level k = 1. We find that the eigenvalue problem of this quantum mechanical system is reduced to the diagonalization of a certain Hankel matrix. In reducing the number of integrations by commuting coordinates and momenta, we find an exact relation concerning the grand partition function, which is interesting on its own right and very helpful for determining the partition function. We also study the TBA-type integral equations that allow us to compute the grand partition function numerically. Surprisingly, all of our exact partition functions are written in terms of polynomials of π −1 with rational coefficients.

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Authors and Affiliations

  1. Department of Physics, Tokyo Institute of Technology, Tokyo, 152-8551, Japan

    Yasuyuki Hatsuda

  2. Kobayashi Maskawa Institute & Graduate School of Mathematics, Nagoya University, Nagoya, 464-8602, Japan

    Sanefumi Moriyama

  3. Department of Physics, Shinshu University, Matsumoto, 390-8621, Japan

    Kazumi Okuyama

Authors
  1. Yasuyuki Hatsuda
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  2. Sanefumi Moriyama
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  3. Kazumi Okuyama
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Correspondence to Sanefumi Moriyama.

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ArXiv ePrint: 1207.4283

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Hatsuda, Y., Moriyama, S. & Okuyama, K. Exact results on the ABJM Fermi gas. J. High Energ. Phys. 2012, 20 (2012). https://doi.org/10.1007/JHEP10(2012)020

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