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Quantization conditions and functional equations in ABJ(M) theories

Publication date2014
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 with consecutive ranks of gauge groups but the same Chern-Simons coupling.

Classification
  • arxiv : hep-th
Note30 pages, 3 figures
Citation (ISO format)
GRASSI, Alba, HATSUDA, Yasuyuki, MARINO BEIRAS, Marcos. Quantization conditions and functional equations in ABJ(M) theories. 2014.
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Creation10/29/2014 10:16:00 AM
First validation10/29/2014 10:16:00 AM
Update time03/14/2023 10:11:00 PM
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