2022-01-17T01:18:08Zhttps://soar-ir.repo.nii.ac.jp/oaioai:soar-ir.repo.nii.ac.jp:000182692021-09-02T06:23:32Z1169:1170Exact results on the ABJM Fermi gasHatsuda, YasuyukiMoriyama, SanefumiOkuyama, KazumiMatrix ModelsChern-Simons TheoriesM-TheoryWe 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 pi(-1) with rational coefficients.ArticleJOURNAL OF HIGH ENERGY PHYSICS. 2012(10):20 (2012)journal articleSPRINGER2012-10application/pdfJOURNAL OF HIGH ENERGY PHYSICS102012201029-8479AA1188279Xhttps://soar-ir.repo.nii.ac.jp/record/18269/files/Exact_results_on_the_ABJM_Fermi_gas.pdfeng10.1007/JHEP10(2012)020https://doi.org/10.1007/JHEP10(2012)020© 2012 SISSA, Trieste, Italy. The final publication is available at link.springer.com