Resurgence provides a unique analytic continuation across natural boundaries for Chern-Simons q-series that matches 3-manifold orientation reversal via Mordell integral decompositions.
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An Introduction to Resurgence, Trans-Series and Alien Calculus
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The all-loop bare perturbative part of the four-quark Bethe-Salpeter kernel is computed analytically in the large-Nf limit of massless QCD.
Exact saddles and finite-T Picard-Lefschetz contour integrals over quasi-zero modes encode the full resurgent structure and yield non-perturbative splittings for every energy level in the double well.
High-energy string amplitudes have asymptotic expansions governed by Bernoulli numbers, upgraded via resurgence to transseries whose Stokes data encode non-perturbative monodromy between kinematic regions.
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.
Resurgent cyclic orbits' algebraic structure plus the leading q-series term determines the asymptotic growth exponent of dual q-series coefficients, which equals an effective central charge c_eff in a related 3d N=2 QFT.
Renormalons can be understood as saddle points of the 1-loop effective action in toy models, enabled by the quantum scale anomaly.
At large chemical potential the Gross-Neveu model enters a crystalline phase in which a-particle bound states condense, producing a periodically oscillating chiral condensate governed by two new scales Λ_n and Λ_c that replace the usual Λ.
Introductory lectures cover resurgent asymptotics using examples like the Airy function, nonlinear Stokes phenomenon, Heisenberg-Euler action, and resurgent continuation.
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Orientation Reversal and the Chern-Simons Natural Boundary
Resurgence provides a unique analytic continuation across natural boundaries for Chern-Simons q-series that matches 3-manifold orientation reversal via Mordell integral decompositions.
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All-loop four-quark Bethe-Salpeter kernel
The all-loop bare perturbative part of the four-quark Bethe-Salpeter kernel is computed analytically in the large-Nf limit of massless QCD.
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Beyond the Dilute Instanton Gas: Resurgence with Exact Saddles in the Double Well
Exact saddles and finite-T Picard-Lefschetz contour integrals over quasi-zero modes encode the full resurgent structure and yield non-perturbative splittings for every energy level in the double well.
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Resurgence of high-energy string amplitudes
High-energy string amplitudes have asymptotic expansions governed by Bernoulli numbers, upgraded via resurgence to transseries whose Stokes data encode non-perturbative monodromy between kinematic regions.
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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.
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$c_{\rm eff}$ from Resurgence at the Stokes Line
Resurgent cyclic orbits' algebraic structure plus the leading q-series term determines the asymptotic growth exponent of dual q-series coefficients, which equals an effective central charge c_eff in a related 3d N=2 QFT.
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Renormalons as Saddle Points
Renormalons can be understood as saddle points of the 1-loop effective action in toy models, enabled by the quantum scale anomaly.
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Perturbative, Nonperturbative and Exact Aspects of Crystalline Phases in the Gross-Neveu Model
At large chemical potential the Gross-Neveu model enters a crystalline phase in which a-particle bound states condense, producing a periodically oscillating chiral condensate governed by two new scales Λ_n and Λ_c that replace the usual Λ.
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Introductory Lectures on Resurgence: CERN Summer School 2024
Introductory lectures cover resurgent asymptotics using examples like the Airy function, nonlinear Stokes phenomenon, Heisenberg-Euler action, and resurgent continuation.
- Picard-Lefschetz theory and alien calculus: a case study
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