Spectral zeta function and non-perturbative effects in ABJM Fermi-gas

Abstract

The exact partition function in ABJM theory on three-sphere can be regarded as a canonical partition function of a non-interacting Fermi-gas with an unconventional Hamiltonian. All the information on the partition function is encoded in the discrete spectrum of this Hamiltonian. We explain how (quantum mechanical) non-perturbative corrections in the Fermi-gas system appear from a spectral consideration. Basic tools in our analysis are a Mellin-Barnes type integral representation and a spectral zeta function. From a consistency with known results, we conjecture that the spectral zeta function in the ABJM Fermi-gas has an infinite number of "non-perturbative" poles, which are invisible in the semi-classical expansion of the Planck constant. We observe that these poles indeed appear after summing up perturbative corrections. As a consequence, the perturbative resummation of the spectral zeta function causes non-perturbative corrections to the grand canonical partition function. We also present another example associated with a spectral problem in topological string theory. A conjectured non-perturbative free energy on the resolved conifold is successfully reproduced in this framework.

32 pages, 4 figures, v2: published version

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• Fractional M2-branes
• Notes on SUSY Gauge Theories on Three-Sphere
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• Probing non-perturbative effects in M-theory
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• Exact ABJM Partition Function from TBA
• Topological Strings and Quantum Spectral Problems
• Resumming the string perturbation series
• M-theoretic matrix models
• Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach
• Exact Instanton Expansion of Superconformal Chern-Simons Theories from Topological Strings
• Finite N from Resurgent Large N
• 3d mirror symmetry as a canonical transformation
• A Note on Instanton Effects in ABJM Theory

Cited by in corpus (22)

• Seiberg-Witten theory as a Fermi gas
• Instanton effects in ABJM theory with general R-charge assignments
• The $\mathcal{N}=2$ Schur index from free fermions
• Resurgence Matches Quantization
• ABJM on ellipsoid and topological strings
• Mathematical structures of non-perturbative topological string theory: from GW to DT invariants
• TBA-like integral equations from quantized mirror curves
• Exact Quantization Conditions, Toric Calabi-Yau and Nonperturbative Topological String
• Localization at large N in Chern-Simons-matter theories
• Orientifolding of the ABJ Fermi gas
• Quantum Curves, Resurgence and Exact WKB
• Exponential Networks, WKB and Topological String
• More on holographic correlators: Twisted and dimensionally reduced structures
• Probing non-perturbative effects in M-theory on orientifolds
• Instanton Corrections of 1/6 BPS Wilson Loops in ABJM Theory
• Spectral determinants and quantum theta functions
• ABJ Theory in the Higher Spin Limit
• Geometric transition in Non-perturbative Topological string
• Mass deformed ABJM and $\mathcal{P}\mathcal{T}$ symmetry
• Exact large $N$ expansion of $\mathcal{N}=4$ circular quiver Chern-Simons theories and squashing
• On refined Chern-Simons / topological string duality for classical gauge groups
• Wilson loops in 3d $\mathcal{N}=4$ SQCD from Fermi gas