Fetching the paper…

Reading the bibliography…

2014

Quantization conditions and functional equations in ABJ(M) theories

Grassi, Alba, Hatsuda, Yasuyuki, Marino, Marcos

Original
PDF
Post on X

Understand

The partition function of ABJ(M) theories on the three-sphere can be regarded as the canonical partition function of an ideal Fermi gas with a non-trivial Hamiltonian.

We propose an exact expression for the spectral determinant of this Hamiltonian, which generalizes recent results obtained in the maximally supersymmetric case.
As a consequence, we find an exact WKB quantization condition determining the spectrum which is in agreement with numerical results.
In addition, we investigate the factorization properties and functional equations for our conjectured spectral determinants.

Quantization conditions and functional equations in ABJ(M) theories · Around

Built on

E. Witten, “Quantum Field Theory and the Jones Polynomial,” Commun. Math. Phys. 121
1989
Earlier work this paper cites.
V. V. Bazhanov, S. L. Lukyanov and A. B. Zamolodchikov, “Integrable structure of conformal field theory. 2. Q operator and DDV equation,” Commun. Math. Phys. 190
1997
Earlier work this paper cites.
P. Dorey and R. Tateo, “Anharmonic oscillators, the thermodynamic Bethe ansatz, and nonlinear integral equations,” J. Phys. A 32
1999
Earlier work this paper cites.
B. Simon, Trace ideals and their applications
2000
Earlier work this paper cites.
V. V. Bazhanov, S. L. Lukyanov and A. B. Zamolodchikov, “Spectral determinants for Schrodinger equation and Q operators of conformal field theory,” J. Statist. Phys. 102
2001
Earlier work this paper cites.
J. Zinn-Justin and U. D. Jentschura, “Multi-instantons and exact results I: Conjectures, WKB expansions, and instanton interactions,” Annals Phys. 313
2004
Earlier work this paper cites.
O. Aharony, O. Bergman, D. L. Jafferis and J. Maldacena, “N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals,” JHEP 0810
Original
2008
Earlier work this paper cites.
O. Aharony, O. Bergman and D. L. Jafferis, “Fractional M2-branes,” JHEP 0811
Original
2008
Earlier work this paper cites.
A. Iqbal, C. Kozcaz and C. Vafa, “The Refined topological vertex,” JHEP 0910
2009
Earlier work this paper cites.
A. Kapustin, B. Willett and I. Yaakov, “Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter,” JHEP 1003
Original
2010
Earlier work this paper cites.
M. Mariño and P. Putrov, “Exact Results in ABJM Theory from Topological Strings,” JHEP 1006
Original
2010
Earlier work this paper cites.
A. Kapustin, B. Willett, I. Yaakov, “Nonperturbative Tests of Three-Dimensional Dualities,” JHEP 1010
Original
2010
Earlier work this paper cites.

Similar

N. Drukker, M. Mariño, P. Putrov, “From weak to strong coupling in ABJM theory,” Commun. Math. Phys. 306
Original
2011
Cited alongside, same era.
C. P. Herzog, I. R. Klebanov, S. S. Pufu and T. Tesileanu, “Multi-Matrix Models and Tri-Sasaki Einstein Spaces,” Phys. Rev. D 83
Original
2011
Cited alongside, same era.
N. Drukker, M. Mariño and P. Putrov, “Nonperturbative aspects of ABJM theory,” JHEP 1111
Original
2011
Cited alongside, same era.
M. Mariño and P. Putrov, “ABJM theory as a Fermi gas,” J. Stat. Mech. 1203
Original
2012
Cited alongside, same era.
Y. Hatsuda, S. Moriyama and K. Okuyama, “Exact Results on the ABJM Fermi Gas,” JHEP 1210
Original

Then

H. Awata, S. Hirano and M. Shigemori, “The Partition Function of ABJ Theory,” Prog. Theor. Exp. Phys. , 053B04 (2013) [arXiv:1212.2966]
Original
2013
Later among the works it cites.
M. Honda, “Direct derivation of ”mirror” ABJ partition function,” JHEP 1312
Original
2013
Later among the works it cites.
Y. Hatsuda, M. Mariño, S. Moriyama and K. Okuyama, “Non-perturbative effects and the refined topological string,” JHEP 1409
Original
2014
Closest in time.
X. f. Wang, X. Wang and M. x. Huang, “A Note on Instanton Effects in ABJM Theory,” JHEP 1411
Original
2014
Closest in time.
M. x. Huang and X. f. Wang, “Topological Strings and Quantum Spectral Problems,” JHEP 1409
Original

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

2012

Cited alongside, same era.

P. Putrov and M. Yamazaki, “Exact ABJM Partition Function from TBA,” Mod. Phys. Lett. A 27

2012

Cited alongside, same era.

A. Voros, “Zeta-regularisation for exact-WKB resolution of a general 1D Schródinger equation,” J. Phys. A 45

2012

Cited alongside, same era.

M. Hanada, M. Honda, Y. Honma, J. Nishimura, S. Shiba and Y. Yoshida, “Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant,” JHEP 1205

2012

Cited alongside, same era.

M. Aganagic, M. C. N. Cheng, R. Dijkgraaf, D. Krefl and C. Vafa, “Quantum Geometry of Refined Topological Strings,” JHEP 1211

2012

Cited alongside, same era.

Y. Hatsuda, S. Moriyama and K. Okuyama, “Instanton Effects in ABJM Theory from Fermi Gas Approach,” JHEP 1301

2013

Cited alongside, same era.

F. Calvo and M. Mariño, “Membrane instantons from a semiclassical TBA,” JHEP 1305

2013

Cited alongside, same era.

Y. Hatsuda, S. Moriyama and K. Okuyama, “Instanton Bound States in ABJM Theory,” JHEP 1305

2013

Cited alongside, same era.

2014

Closest in time.

S. Matsumoto and S. Moriyama, “ABJ Fractional Brane from ABJM Wilson Loop,” JHEP 1403

2014

Closest in time.

M. Honda and K. Okuyama, “Exact results on ABJ theory and the refined topological string,” JHEP 1408

2014

Closest in time.

Y. Hatsuda and K. Okuyama, “Probing non-perturbative effects in M-theory,” JHEP 1410

2014

Closest in time.

J. Choi, S. Katz and A. Klemm, “The refined BPS index from stable pair invariants,” Commun. Math. Phys. 328

Original

2014

Closest in time.

J. Kallen, “The spectral problem of the ABJ Fermi gas,” JHEP 1510

2015

Closest in time.

S. Codesido, A. Grassi and M. Mariño, “Exact results in 𝒩 = 8 \mathcal{N}=8 Chern-Simons-matter theories and quantum geometry,” JHEP 1507

Original

2015

Closest in time.