Exact Results on the ABJM Fermi Gas

Abstract

We study the Fermi gas quantum mechanics associated to the ABJM matrix model. We develop the method to compute the grand partition function of the ABJM theory, and compute exactly the partition function Z(N) up to N=9 when 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 results of the partition functions are written in terms of polynomials of 1/pi with rational coefficients.

41 pages, 4 figures

References in corpus (8)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Fractional M2-branes
• Summing Up All Genus Free Energy of ABJM Matrix Model
• Supersymmetry enhancement by monopole operators
• Anomalous radius shift in AdS(4)/CFT(3)
• Notes on Supersymmetry Enhancement of ABJM Theory
• ABJM Wilson loops in the Fermi gas approach
• Interacting fermions and N=2 Chern-Simons-matter theories

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