2024-03-28T12:30:32Z
https://soar-ir.repo.nii.ac.jp/oai
oai:soar-ir.repo.nii.ac.jp:00018269
2022-12-14T04:13:24Z
1169:1170
Exact results on the ABJM Fermi gas
Hatsuda, Yasuyuki
Moriyama, Sanefumi
Okuyama, Kazumi
© 2012 SISSA, Trieste, Italy. The final publication is available at link.springer.com
Matrix Models
Chern-Simons Theories
M-Theory
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 pi(-1) with rational coefficients.
Article
JOURNAL OF HIGH ENERGY PHYSICS. 2012(10):20 (2012)
SPRINGER
2012-10
eng
journal article
AM
http://hdl.handle.net/10091/00019031
https://soar-ir.repo.nii.ac.jp/records/18269
https://doi.org/10.1007/JHEP10(2012)020
10.1007/JHEP10(2012)020
1029-8479
AA1188279X
JOURNAL OF HIGH ENERGY PHYSICS
2012
10
20
https://soar-ir.repo.nii.ac.jp/record/18269/files/Exact_results_on_the_ABJM_Fermi_gas.pdf
application/pdf
401.9 kB
2016-08-19