# 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} }

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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