Cluster expansion and resurgence in Polyakov model

Abstract

In Polyakov model, a non-perturbative mass gap is formed at leading order semi-classics by instanton effects. By using the notions of critical points at infinity, cluster expansion and Lefschetz thimbles, we show that a third order effect in semi-classics gives an imaginary ambiguous contribution to mass gap, which is supposed to be real and unambiguous. This is troublesome for the original analysis, and it is difficult to resolve this issue directly in QFT. However, we find a new compactification of Polyakov model to quantum mechanics, by using a background 't Hooft flux (or coupling to TQFT). The compactification has the merit of remembering the monopole-instantons of the full QFT within Born-Oppenheimer (BO) approximation, while the periodic compactification does not. In QM, we prove the resurgent cancellation of the ambiguity in 3-instanton sector against ambiguity in the Borel resummation of the perturbation theory around 1-instanton. Assuming that this result holds in QFT, we provide a large-order asymptotics of perturbation theory around perturbative vacuum and instanton.

arXiv comment6 pages, 1 figure

References in corpus (36)

• Coupling a QFT to a TQFT and Duality
• Theta, Time Reversal, and Temperature
• Resurgence and Trans-series in Quantum Field Theory: The CP(N-1) Model
• Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
• The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
• Uniform WKB, Multi-instantons, and Resurgent Trans-Series
• Generating Non-perturbative Physics from Perturbation Theory
• Resurgence theory, ghost-instantons, and analytic continuation of path integrals
• New Methods in QFT and QCD: From Large-N Orbifold Equivalence to Bions and Resurgence
• Theta dependence, sign problems and topological interference
• Seiberg-Witten and "Polyakov-like" magnetic bion confinements are continuously connected
• Neutral bions in the $\mathbb{C}{P}^{N-1}$ model
• Hidden topological angles and Lefschetz thimbles
• Global inconsistency, 't Hooft anomaly, and level crossing in quantum mechanics
• Microscopic Structure of Magnetic Bions
• Classifying bions in Grassmann sigma models and non-Abelian gauge theories by D-branes
• Bion non-perturbative contributions versus infrared renormalons in two-dimensional $\mathbb{C}{P}^{N-1}$ models
• Investigating Yang-Mills theory and Confinement as a function of the spatial volume
• Exact Resurgent Trans-series and Multi-Bion Contributions to All Orders
• Gauge invariant structures and Confinement
• Numerical Stochastic Perturbation Theory for full QCD
• Numerical study of Yang-Mills classical solutions on the twisted torus
• On exact-WKB analysis, resurgent structure, and quantization conditions
• Renormalons in integrable field theories
• Resurgence Structure to All Orders of Multi-bions in Deformed SUSY Quantum Mechanics
• Non-BPS exact solutions and their relation to bions in $\mathbb{C}{P}^{N-1}$ models
• Critical Points at Infinity, Non-Gaussian Saddles, and Bions
• Constructing SU(N) fractional instantons
• Testing the Bethe ansatz with large N renormalons
• From Perturbation Theory to Confinement: How the String Tension is built up
• Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: ${\varphi }^3$ QFT in 6 Dimensions
• The abelian confinement mechanism revisited: new aspects of the Georgi-Glashow model
• Four-loop lattice-regularized vacuum energy density of the three-dimensional SU(3) + adjoint Higgs theory
• Identification of perturbative ambiguity canceled against bion
• Numerical stochastic perturbation theory applied to the twisted Eguchi-Kawai model
• QCD in a Finite Volume

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• Notes on Confinement on ${\mathbf{R}}^3\times {\mathbf{S}}^1$: From Yang-Mills, super-Yang-Mills, and QCD(adj) to QCD(F)
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• Exact WKB in all sectors I: Potentials with degenerate saddles
• Exact-WKB Analysis of Two-level Floquet Systems
• Exact WKB in all sectors II: Potentials with non-degenerate saddles
• Polyakov Model in 't Hooft flux background: A quantum mechanical reduction with memory