Exact results on the ABJM Fermi gas

By Yasuyuki Hatsuda, Sanefumi Moriyama, Kazumi Okuyama. 2012

136 citations recorded by the source corpus.

A bstractWe 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.

Subfields: Applied Mathematics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/b7c1da559a87358f456b30908c706477ce8e7088

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In Applied Mathematics

1. Yasuyuki Hatsuda
2. Kazumi Okuyama
3. Sanefumi Moriyama
4. Marcos Mariño
5. A. Grassi
6. C. Vafa

In Geometry and Topology

1. Yasuyuki Hatsuda
2. Sanefumi Moriyama
3. Kazumi Okuyama
4. A. Grassi
5. Marcos Mariño
6. C. Vafa
7. Mina Aganagic
8. Pavel Putrov

In Nuclear and High Energy Physics

1. Yasuyuki Hatsuda
2. Sanefumi Moriyama
3. Kazumi Okuyama
4. A. Grassi
5. Marcos Mariño
6. C. Vafa
7. Pavel Putrov
8. B. Eynard

Citations in the corpus

• Instanton bound states in ABJM theory (2013, methodology): “In [16, 17], the exact ABJM partition function at k = 1 was computed up to some values of N .”
• Non-perturbative effects and the refined topological string (2013, background): “This makes it possible to calculate the partition function Z(N, k) for small values of N [13, 14].”
• Topological Strings from Quantum Mechanics (2014, methodology): “(4)In the case of ABJM theory, it is possible to obtain an explicit form for the integral kernel of ρ̂, and one can use standard techniques for the computation of the eigenvalues and eigenfunctions of such kernels, see [6, 11].”
• Instanton effects in ABJM theory from Fermi gas approach (2012, methodology): “We generalize our previous method in [13] to arbitrary level k.”