Heisenberg-Euler effective Lagrangian is recast as a dispersion integral with the quantum dilogarithm as kernel, its imaginary part given directly by the dilogarithm and its real part involving the modular dual.
Resummations and Non-Perturbative Corrections
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abstract
We consider a generalization of the Borel resummation, which turns out to be equivalent to the standard Borel resummation. We apply it to the simplest large N duality between the pure Chern-Simons theory and the topological string on the resolved conifold, and find a simple integral formula for the free energy. Expanding this integral representation around the large radius point at finite string coupling gs, we find that it includes not only the M-theoretic resummation a la Gopakumar and Vafa, but also a non-perturbative correction in gs. Remarkably, the obtained non-perturbative correction is in perfect agreement with a proposal for membrane instanton corrections in arXiv:1306.1734. Various other examples are also presented.
fields
hep-th 3representative citing papers
Topological string partition function on CY threefolds factors into conifold terms powered by sheaf invariants, enabling non-perturbative Borel-resummed expression whose jumps are controlled by genus-zero GV invariants and a deformed prepotential.
Inhomogeneous background fields convert Borel poles in the effective action to branch points and introduce new ones, allowing resurgent extrapolation to recover non-perturbative information from perturbative input more accurately than WKB or locally constant approximations.
citing papers explorer
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Heisenberg-Euler and the Quantum Dilogarithm
Heisenberg-Euler effective Lagrangian is recast as a dispersion integral with the quantum dilogarithm as kernel, its imaginary part given directly by the dilogarithm and its real part involving the modular dual.
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Non-perturbative topological strings from resurgence
Topological string partition function on CY threefolds factors into conifold terms powered by sheaf invariants, enabling non-perturbative Borel-resummed expression whose jumps are controlled by genus-zero GV invariants and a deformed prepotential.
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Resurgence of the Effective Action in Inhomogeneous Fields
Inhomogeneous background fields convert Borel poles in the effective action to branch points and introduce new ones, allowing resurgent extrapolation to recover non-perturbative information from perturbative input more accurately than WKB or locally constant approximations.