The spectral problem of the ABJ Fermi gas

Abstract

The partition function on the three-sphere of ABJ theory can be rewritten into a partition function of a non-interacting Fermi gas, with an accompanying one-particle Hamiltonian. We study the spectral problem defined by this Hamiltonian. We determine the exact WKB quantization condition, which involves quantities from refined topological string theory, and test it successfully against numerical calculations of the spectrum.

arXiv comment31 pages

References in corpus (15)

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• Nekrasov Functions and Exact Bohr-Sommerfeld Integrals
• Lectures on non-perturbative effects in large N gauge theories, matrix models and strings
• ABJM theory as a Fermi gas
• Non-perturbative effects and the refined topological string
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• Conformal Matrix Models as an Alternative to Conventional Multi-Matrix Models
• D-particles, Matrix Integrals and KP hierachy
• Nekrasov Functions from Exact BS Periods: the Case of SU(N)
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• Direct derivation of "mirror" ABJ partition function
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Cited by in corpus (8)

• Resurgence and the Nekrasov-Shatashvili Limit: Connecting Weak and Strong Coupling in the Mathieu and Lam'e Systems
• Probing non-perturbative effects in M-theory
• Partition functions of 3d $\hat{D}$-quivers and their mirror duals from 1d free fermions
• Exact results in N=8 Chern-Simons-matter theories and quantum geometry
• Exact Instanton Expansion of ABJM Partition Function
• ABJM Membrane Instanton from Pole Cancellation Mechanism
• On Perturbation theory improved by Strong coupling expansion
• Resurgence and Dynamics of O(N) and Grassmannian Sigma Models