Resurgence provides a unique analytic continuation across natural boundaries for Chern-Simons q-series that matches 3-manifold orientation reversal via Mordell integral decompositions.
Resurgence in complex Chern-Simons theory
8 Pith papers cite this work. Polarity classification is still indexing.
8
Pith papers citing it
abstract
We study resurgence properties of partition function of SU(2) Chern-Simons theory (WRT invariant) on closed three-manifolds. We check explicitly that in various examples Borel transforms of asymptotic expansions posses expected analytic properties. In examples that we study we observe that contribution of irreducible flat connections to the path integral can be recovered from asymptotic expansions around abelian flat connections. We also discuss connection to Floer instanton moduli spaces, disk instantons in 2d sigma models, and length spectra of "complex geodesics" on the A-polynomial curve.
representative citing papers
An extended square matrix of (x,q)-series indexed by boundary parabolic SL2(C) flat connections completely describes the resurgent structure, Stokes constants, and Borel transform of Chern-Simons perturbation theory at the trivial flat connection for hyperbolic knot complements.
Establishes explicit resurgent duality between zero-radius weak-coupling and infinite-radius strong-coupling expansions, illustrated on Airy/Pearcey integrals and applied to phi^4 Dyson-Schwinger equations and Gross-Neveu kink-antikink heat kernel.
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.
Extends operator formalism of closed topological strings to derive all-order trans-series solutions for real topological strings, with disk invariants as Stokes constants and numerical checks on local P2.
Mock theta functions admit a unique resurgent continuation across their natural boundary, with the continuation fixed by their Mordell-Appell integrals via rotated Laplace contours.
It conjectures that the E_2-category arising from BV-BFV quantization of Chern-Simons on the disk supplies the modular tensor category for Reshetikhin-Turaev invariants, with derived character stacks Loc_G(Σ) mediating an equivalence of (3-2-1)-extended TQFTs.
Alexander polynomials appear in two opposite roles in two Kashaev phases of Chern-Simons theory due to co-existing branches in the quasiclassical limit with non-trivial versus vanishing classical actions.
citing papers explorer
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Resurgence of Chern-Simons theory at the trivial flat connection
An extended square matrix of (x,q)-series indexed by boundary parabolic SL2(C) flat connections completely describes the resurgent structure, Stokes constants, and Borel transform of Chern-Simons perturbation theory at the trivial flat connection for hyperbolic knot complements.
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Weak-Strong Resurgence Duality
Establishes explicit resurgent duality between zero-radius weak-coupling and infinite-radius strong-coupling expansions, illustrated on Airy/Pearcey integrals and applied to phi^4 Dyson-Schwinger equations and Gross-Neveu kink-antikink heat kernel.
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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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Non-Perturbative Real Topological Strings
Extends operator formalism of closed topological strings to derive all-order trans-series solutions for real topological strings, with disk invariants as Stokes constants and numerical checks on local P2.
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On Uniqueness of Mock Theta Functions
Mock theta functions admit a unique resurgent continuation across their natural boundary, with the continuation fixed by their Mordell-Appell integrals via rotated Laplace contours.
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From BV-BFV Quantization to Reshetikhin-Turaev Invariants
It conjectures that the E_2-category arising from BV-BFV quantization of Chern-Simons on the disk supplies the modular tensor category for Reshetikhin-Turaev invariants, with derived character stacks Loc_G(Σ) mediating an equivalence of (3-2-1)-extended TQFTs.
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Two roles of Alexander in two Kashaev phases
Alexander polynomials appear in two opposite roles in two Kashaev phases of Chern-Simons theory due to co-existing branches in the quasiclassical limit with non-trivial versus vanishing classical actions.