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I. R. Klebanov and A. A. Tseytlin, “Entropy of near extremal black p-branes,” Nucl. Phys. B 475
1996
Earlier work this paper cites.
C. A. Tracy and H. Widom, “Proofs of two conjectures related to the thermodynamic Bethe ansatz,” Commun. Math. Phys. 179
1996
Earlier work this paper cites.
S. H. Katz, A. Klemm and C. Vafa, “M theory, topological strings and spinning black holes,” Adv. Theor. Math. Phys. 3
1999
Earlier work this paper cites.
M. Marino, “Chern-Simons theory, matrix integrals, and perturbative three manifold invariants,” Commun. Math. Phys. 253
2004
Earlier work this paper cites.
M. Aganagic, A. Klemm, M. Marino and C. Vafa, “Matrix model as a mirror of Chern-Simons theory,” JHEP 0402
2004
Earlier work this paper cites.
M. Aganagic, M. Marino and C. Vafa, “All loop topological string amplitudes from Chern-Simons theory,” Commun. Math. Phys. 247
2004
Earlier work this paper cites.
H. Ooguri, C. Vafa and E. P. Verlinde, “Hartle-Hawking wave-function for flux compactifications,” Lett. Math. Phys. 74
2005
Earlier work this paper cites.

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2012

Hatsuda, Yasuyuki, Moriyama, Sanefumi, Okuyama, Kazumi

We study the instanton effects of the ABJM partition function using the Fermi gas formalism.

We compute the exact values of the partition function at the Chern-Simons levels k=1,2,3,4,6 up to N=44,20,18,16,14 respectively, and extract non-perturbative corrections from these exact results.
Fitting the resulting non-perturbative corrections by their expected forms from the Fermi gas, we determine unknown parameters in them.
After separating the oscillating behavior of the grand potential, which originates in the periodicity of the grand partition function, and the worldsheet instanton contribution, which is computed from the topological string theory, we succeed in proposing an analytical expression for the leading D2-instanton correction.

I. R. Klebanov and A. A. Tseytlin, “Entropy of near extremal black p-branes,” Nucl. Phys. B 475
1996
Earlier work this paper cites.
C. A. Tracy and H. Widom, “Proofs of two conjectures related to the thermodynamic Bethe ansatz,” Commun. Math. Phys. 179
1996
Earlier work this paper cites.
S. H. Katz, A. Klemm and C. Vafa, “M theory, topological strings and spinning black holes,” Adv. Theor. Math. Phys. 3
1999
Earlier work this paper cites.
M. Marino, “Chern-Simons theory, matrix integrals, and perturbative three manifold invariants,” Commun. Math. Phys. 253
2004
Earlier work this paper cites.
M. Aganagic, A. Klemm, M. Marino and C. Vafa, “Matrix model as a mirror of Chern-Simons theory,” JHEP 0402
2004
Earlier work this paper cites.
M. Aganagic, M. Marino and C. Vafa, “All loop topological string amplitudes from Chern-Simons theory,” Commun. Math. Phys. 247
2004
Earlier work this paper cites.
H. Ooguri, C. Vafa and E. P. Verlinde, “Hartle-Hawking wave-function for flux compactifications,” Lett. Math. Phys. 74
2005
Earlier work this paper cites.