REVIEW 16 cited by
An Introduction to Resurgence, Trans-Series and Alien Calculus
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
An Introduction to Resurgence, Trans-Series and Alien Calculus
read the original abstract
In these notes we give an overview of different topics in resurgence theory from a physics point of view, but with particular mathematical flavour. After a short review of the standard Borel method for the resummation of asymptotic series, we introduce the class of simple resurgent functions, explaining their importance in physical problems. We define the Stokes automorphism and the alien derivative and discuss these objects in concrete examples using the notion of trans-series expansion. With all the tools introduced, we see how resurgence and alien calculus allow us to extract non-perturbative physics from perturbation theory. To conclude, we apply Morse theory to a toy model path integral to understand why physical observables should be resurgent functions.
Forward citations
Cited by 16 Pith papers
-
Massive Cosmological Correlators from Flat Space: a Laplace-Space Approach
A Laplace-space representation converts massive single-exchange cosmological correlators in de Sitter into a rapidly convergent series derived from flat-space integrals.
-
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.
-
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.
-
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.
-
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.
-
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 mor...
-
Positivity properties of observables in planar maximally supersymmetric Yang-Mills theory
Several observables in planar N=4 SYM, including the octagon anomalous dimension and Bremsstrahlung function, admit a once-subtracted dispersion representation over a positive measure in the coupling.
-
Universal global analytic expansion for the 't Hooft-Polyakov monopole profiles
Develops a global analytic expansion for 't Hooft-Polyakov monopole profiles around universal non-perturbative background functions, matching known local behaviors at zero and infinite radii.
-
Picard-Lefschetz theory and alien calculus: a case study
Explicit calculations in the Airy, Bessel, and Gamma models show that Lefschetz thimble wall-crossing produces the same Stokes coefficients as alien operators acting on Borel singularities.
-
Strong coupling structure of $\mathcal{N}=4$ SYM observables with matrix Bessel kernel
Reorganizing the transseries of matrix Bessel kernel determinants at strong coupling yields a simple structure where non-perturbative corrections are directly determined by the perturbative series for N=4 SYM observables.
-
$c_{\rm eff}$ 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.
-
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.
-
Picard-Lefschetz theory and alien calculus: a case study
Compares Lefschetz thimbles and alien operators in Airy, Bessel, and Gamma models to recover matching Stokes coefficients as test cases for their correspondence.
-
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 tha...
-
The Double Well Done Doubly-Well
Presents explicit trans-series calculations for the double-well spectrum via exact WKB and path integral approaches up to four-instanton level.
-
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.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.