Quantization conditions and functional equations in ABJ(M) theories

@article{Grassi2014QuantizationCA,
  title={Quantization conditions and functional equations in ABJ(M) theories},
  author={A. Grassi and Y. Hatsuda and M. Mari{\~n}o},
  journal={Journal of Physics A},
  year={2014},
  volume={49},
  pages={115401}
}
  • A. Grassi, Y. Hatsuda, M. Mariño
  • Published 2014
  • Physics, Mathematics
  • Journal of Physics A
  • 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 nd an exact WKB quantization condition determining the spectrum which is in agreement with numerical results. In addition, we investigate the… CONTINUE READING

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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 41 REFERENCES
    Exact results on the ABJM Fermi gas
    94
    The spectral problem of the ABJ Fermi gas
    21
    ABJM theory as a Fermi gas
    250
    Direct derivation of “mirror” ABJ partition function
    54
    A note on instanton effects in ABJM theory
    18
    Anharmonic oscillators, the thermodynamic Bethe ansatz and nonlinear integral equations
    143
    Exact results for Wilson loops in superconformal Chern-Simons theories with matter
    788
    Non-perturbative effects and the refined topological string
    168
    ABJ fractional brane from ABJM Wilson loop
    72