Quantization conditions and functional equations in ABJ(M) theories. (8th February 2016)

• Record Type: Journal Article
• Authors: Grassi, Alba; Hatsuda, Yasuyuki; Mariño, Marcos
• Is Part Of: Journal of physics. Volume 49:Number 11(2016)
• Publication Date: 2016-02-08
• Subjects: ABJ(M) theories -- non-perturbative effects -- spectral determinant; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8113/49/11/115401
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: 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. These functional equations relate the spectral determinants of ABJ theories to consecutive ranks of gauge groups but the same Chern–Simons coupling.