Quantization conditions and functional equations in ABJ(M) theories

摘要: The partition function of ABJ(M) theories on the three-sphere can be regarded as canonical an ideal Fermi gas with a non-trivial Hamiltonian. We propose exact expression for spectral determinant this Hamiltonian, which generalizes recent results obtained in maximally supersymmetric case. As consequence, we nd WKB quantization condition determining spectrum is agreement numerical results. In addition, investigate factorization properties and functional equations our conjectured determinants. These relate determinants ABJ consecutive ranks gauge groups but same Chern-Simons coupling.