Resurgence in QFT: Unitons, Fractons and Renormalons in the Principal Chiral Model

Abstract

We explain the physical role of non-perturbative saddle points of path integrals in theories without instantons, using the example of the asymptotically free two-dimensional principal chiral model (PCM). Standard topological arguments based on homotopy considerations suggest no role for non-perturbative saddles in such theories. However, resurgence theory, which unifies perturbative and non-perturbative physics, predicts the existence of several types of non-perturbative saddles associated with features of the large-order structure of perturbation theory. These points are illustrated in the PCM, where we find new non-perturbative `fracton' saddle point field configurations, and give a quantum interpretation of previously discovered `uniton' unstable classical solutions. The fractons lead to a semi-classical realization of IR renormalons in the circle-compactified theory, and yield the microscopic mechanism of the mass gap of the PCM.

v2: references added

References in corpus (5)

• Center-stabilized Yang-Mills theory: confinement and large $N$ volume independence
• Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
• Instanton constituents in the O(3) model at finite temperature
• Revisiting the Faddeev-Skyrme Model and Hopf Solitons
• Correlation Functions of the SU(infinity) Principal Chiral Model

Cited by in corpus (96)

• A Primer on Resurgent Transseries and Their Asymptotics
• An Introduction to Resurgence, Trans-Series and Alien Calculus
• Hamiltonian Truncation Study of the Phi^4 Theory in Two Dimensions
• Nonperturbative Ambiguities and the Reality of Resurgent Transseries
• New Methods in QFT and QCD: From Large-N Orbifold Equivalence to Bions and Resurgence
• Anomaly and global inconsistency matching: $\theta$-angles, $SU(3)/U(1{)}^2$ nonlinear sigma model, $SU(3)$ chains and its generalizations
• Modified instanton sum in QCD and higher-groups
• Vacuum structure of bifundamental gauge theories at finite topological angles
• Circle compactification and 't Hooft anomaly
• Hydrodynamics, resurgence and trans-asymptotics
• Neutral bions in the $\mathbb{C}{P}^{N-1}$ model
• Toward Picard-Lefschetz Theory of Path Integrals, Complex Saddles and Resurgence
• Cheshire Cat resurgence, Self-resurgence and Quasi-Exact Solvable Systems
• Deconstructing zero: resurgence, supersymmetry and complex saddles
• Non-perturbative Contributions from Complexified Solutions in $\mathbb{C}{P}^{N-1}$ Models
• Resumming the string perturbation series
• From 4d Yang-Mills to 2d ${\mathbb{CP}}^{N-1}$ model: IR problem and confinement at weak coupling
• Global inconsistency, 't Hooft anomaly, and level crossing in quantum mechanics
• Resurgence in sine-Gordon quantum mechanics: Exact agreement between multi-instantons and uniform WKB
• Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral
• Classifying bions in Grassmann sigma models and non-Abelian gauge theories by D-branes
• Chiral Lagrangian from Duality and Monopole Operators in Compactified QCD
• Bion non-perturbative contributions versus infrared renormalons in two-dimensional $\mathbb{C}{P}^{N-1}$ models
• Perturbative expansion of the plaquette to $\mathcal{O}({\alpha }^{35})$ in four-dimensional SU(3) gauge theory
• Complex Saddles in Two-dimensional Gauge Theory
• Exact Resurgent Trans-series and Multi-Bion Contributions to All Orders
• O(3) nonlinear sigma model in 1+1 dimensions with matrix product states
• Borel summability of perturbative series in 4d N=2 and 5d N=1 theories
• Resurgence of the Cusp Anomalous Dimension
• Dual lattice representations for O(N) and CP(N-1) models with a chemical potential
• Resurgence in $\eta$-deformed Principal Chiral Models
• Quantum Distillation of Hilbert Spaces, Semi-classics and Anomaly Matching
• The Resurgence of the Cusp Anomalous Dimension
• Fractional instantons and bions in the O(N) model with twisted boundary conditions
• Renormalons in integrable field theories
• The curious incident of multi-instantons and the necessity of Lefschetz thimbles
• Remark on the Dunne-Unsal relation in exact semi-classics
• Exact-WKB, complete resurgent structure, and mixed anomaly in quantum mechanics on $S^1$
• How to resum perturbative series in 3d N=2 Chern-Simons matter theories
• Non-BPS exact solutions and their relation to bions in $\mathbb{C}{P}^{N-1}$ models
• Resurgence Structure to All Orders of Multi-bions in Deformed SUSY Quantum Mechanics
• Non-perturbative aspects of the self-dual double copy
• Resurgence in the O(4) sigma model
• Critical Points at Infinity, Non-Gaussian Saddles, and Bions
• Fractional instantons and bions in the principal chiral model on ${\mathbb{R}}^2\times S^1$ with twisted boundary conditions
• Modular-invariant large-$N$ completion of an integrated correlator in $\mathcal{N}=4$ supersymmetric Yang-Mills theory
• Resurgence of the Renormalization Group Equation
• Constructing SU(N) fractional instantons
• Resurgence for superconductors
• Generating a non-perturbative mass gap using Feynman diagrams in an asymptotically free theory
• New renormalons from analytic trans-series
• On Perturbation theory improved by Strong coupling expansion
• The two-dimensional O(3) model at nonzero density: from dual lattice simulations to repulsive bosons
• Phase structure of the twisted $SU(3)/U(1{)}^2$ flag sigma model on $\mathbb{R}\times S^1$
• Neutral bions in the CP^{N-1} model for resurgence
• Nonlinear sigma models at nonzero chemical potential: breaking up instantons and the phase diagram
• Resurgence and renormalons in the one-dimensional Hubbard model
• Topology and $\theta$ dependence in finite temperature $G_2$ lattice gauge theory
• Universal Renormalons in Principal Chiral Models
• Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles
• Lattice $\mathbb{C}{P}^{N-1}$ model with ${\mathbb{Z}}_N$ twisted boundary condition: bions, adiabatic continuity and pseudo-entropy
• A Schwinger--Dyson Equation in the Borel Plane: singularities of the solution
• A new renormalon in two dimensions
• Clustering and decomposition for non BPS solutions of the ${\mathbb{CP}}^{N-1}$ models
• Instantons, renormalons and the theta angle in integrable sigma models
• Resurgence in Lorentzian quantum cosmology: No-boundary saddles and resummation of quantum gravity corrections around tunneling saddle points
• SUSY breaking by nonperturbative dynamics in a matrix model for 2D type IIA superstrings
• Interpolating function and Stokes Phenomena
• Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED
• Resurgence and Lefschetz thimble in 3d N=2 supersymmetric Chern-Simons matter theories
• Resumming perturbative series in the presence of monopole bubbling effects
• Renormalons beyond the Borel plane
• Resurgent Analysis of Localizable Observables in Supersymmetric Gauge Theories
• High order perturbation theory for difference equations and Borel summability of quantum mirror curves
• Renormalons in quantum mechanics
• Reconstruction of spectra and an algorithm based on the theorems of Darboux and Puiseux
• Symmetry improvement of 3PI effective actions for O(N) scalar field theory
• S-duality Improved Perturbation Theory in Compactified Type I / Heterotic String Theory
• Seeing asymptotic freedom in an exact correlator of a large-$N$ matrix field theory
• Analyticity domain of a Quantum Field Theory and Accelero-summation
• Dynamical Mass Reduction in the Massive Yang-Mills Spectrum in 1+1 dimensions
• Planar quantum quenches: Computation of exact time-dependent correlation functions at large $N$
• Resurgence and semiclassical expansion in two-dimensional large-$N$ sigma models
• Asymptotics in an Asymptotic CFT
• Nontrivial Thermodynamics in 't Hooft's Large-$N$ Limit
• The two-dimensional twisted reduced principal chiral model revisited
• Resurgence and Dynamics of O(N) and Grassmannian Sigma Models
• Resurgence of one-point functions in a matrix model for 2D type IIA superstrings
• The Compactified Principal Chiral Model's Mass Gap
• Fermion scattering on topological solitons in the ${\mathbb{CP}}^{N-1}$ model
• Resurgence and $1/N$ Expansion in Integrable Field Theories
• Two-point functions at arbitrary genus and its resurgence structure in a matrix model for 2D type IIA superstrings
• Diagrammatic Monte-Carlo for weak-coupling expansion of non-Abelian lattice field theories: large-N U(N)xU(N) principal chiral model
• Confinement-Higgs Phase Crossover as a Lattice Artifact in 1+1 Dimensions
• Nonperturbative features in the Lie-algebraic Kähler sigma model with fermions
• On Lagrangian description of Borel resummation