Resurgence and Trans-series in Quantum Field Theory: The CP(N-1) Model

Abstract

This work is a step towards a non-perturbative continuum definition of quantum field theory (QFT), beginning with asymptotically free two dimensional non-linear sigma-models, using recent ideas from mathematics and QFT. The ideas from mathematics are resurgence theory, the trans-series framework, and Borel-Ecalle resummation. The ideas from QFT use continuity on R^1 x S^1_L, i.e, the absence of any phase transition as N \to infinity, or rapid-crossovers for finite-N, and the small-L weak coupling limit to render the semi-classical sector well-defined and calculable. We classify semi-classical configurations with actions 1/N (kink-instantons), 2/N (bions and bi-kinks), in units where the 2d instanton action is normalized to one. Perturbation theory possesses the IR-renormalon ambiguity that arises due to non-Borel summability of the large-orders perturbation series (of Gevrey-1 type), for which a microscopic cancellation mechanism was unknown. This divergence must be present because the corresponding expansion is on a singular Stokes ray in the complexified coupling constant plane, and the sum exhibits the Stokes phenomenon crossing the ray. We show that there is also a non-perturbative ambiguity inherent to certain neutral topological molecules (neutral bions and bion-anti-bions) in the semiclassical expansion. We find a set of "confluence equations" that encode the exact cancellation of the two different type of ambiguities. We show that a new notion of "graded resurgence triangle" is necessary to capture the path integral approach to resurgence, and that graded resurgence underlies a potentially rigorous definition of general QFTs. The mass gap and the Theta angle dependence of vacuum energy are calculated from first principles, and are in accord with large-N and lattice results.

89 pages; 13 figures

References in corpus (16)

• Lectures on non-perturbative effects in large N gauge theories, matrix models and strings
• Center-stabilized Yang-Mills theory: confinement and large $N$ volume independence
• Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
• Volume independence in large Nc QCD-like gauge theories
• The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
• Abelian duality, confinement, and chiral symmetry breaking in QCD(adj)
• Magnetic Monopole Dynamics, Supersymmetry, and Duality
• Continuity, Deconfinement, and (Super) Yang-Mills Theory
• Continuity and Resurgence: towards a continuum definition of the CP(N-1) model
• Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
• New Phases of SU(3) and SU(4) at Finite Temperature
• Instanton constituents in the O(3) model at finite temperature
• The Partonic Nature of Instantons
• Large-order Perturbation Theory and de Sitter/Anti de Sitter Effective Actions
• Perturbative Aspects of Heterotically Deformed CP(N-1) Sigma Model. I
• Theta-vacuum and large N limit in CP^{N-1} sigma models

Cited by in corpus (197)

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• An Introduction to Resurgence, Trans-Series and Alien Calculus
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• Generating Non-perturbative Physics from Perturbation Theory
• Nonperturbative Ambiguities and the Reality of Resurgent Transseries
• Continuity and Resurgence: towards a continuum definition of the CP(N-1) model
• Resurgence in QFT: Unitons, Fractons and Renormalons in the Principal Chiral Model
• 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
• Anomaly and global inconsistency matching: $\theta$-angles, $SU(3)/U(1{)}^2$ nonlinear sigma model, $SU(3)$ chains and its generalizations
• Entropy Production, Hydrodynamics, and Resurgence in the Primordial Quark-Gluon Plasma from Holography
• Resurgence and the Nekrasov-Shatashvili Limit: Connecting Weak and Strong Coupling in the Mathieu and Lam'e Systems
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• Anomaly matching for phase diagram of massless ${\mathbb{Z}}_N$-QCD
• Structure of Lefschetz thimbles in simple fermionic systems
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• Resurgence in Extended Hydrodynamics
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• Circle compactification and 't Hooft anomaly
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• Hidden topological angles and Lefschetz thimbles
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• Non-perturbative Contributions from Complexified Solutions in $\mathbb{C}{P}^{N-1}$ Models
• Physical Resurgent Extrapolation
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• Deconfinement and continuity between thermal and (super) Yang-Mills theory for all gauge groups
• Higgs Physics: It ain't over till it's over
• Resurgence in complex Chern-Simons theory
• 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
• Harnessing S-Duality in $\mathcal{N}=4$ SYM & Supergravity as $SL(2,\mathbb{Z})$-Averaged Strings
• 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
• On the Late-Time Behavior of Virasoro Blocks and a Classification of Semiclassical Saddles
• Perturbative expansion of the plaquette to $\mathcal{O}({\alpha }^{35})$ in four-dimensional SU(3) gauge theory
• Probing Baryogenesis through the Higgs Self-Coupling
• Complex Saddles in Two-dimensional Gauge Theory
• (S)QCD on R^3 x S^1: Screening of Polyakov loop by fundamental quarks and the demise of semi-classics
• Exact Resurgent Trans-series and Multi-Bion Contributions to All Orders
• Fractional $\theta$ angle, 't Hooft anomaly, and quantum instantons in charge-$q$ multi-flavor Schwinger model
• The grin of Cheshire cat resurgence from supersymmetric localization
• Center vortex and confinement in Yang-Mills theory and QCD with anomaly-preserving compactifications
• 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
• Dual lattice representations for O(N) and CP(N-1) models with a chemical potential
• Deconfinement in N=1 super Yang-Mills theory on R^3 x S^1 via dual-Coulomb gas and "affine" XY-model
• Resurgence in $\eta$-deformed Principal Chiral Models
• New Higher Anomalies, SU(N) Yang-Mills Gauge Theory and ${\mathbb{CP}}^{\mathrm{N}-1}$ Sigma Model
• RG-Whitham dynamics and complex Hamiltonian systems
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• Quantum Distillation of Hilbert Spaces, Semi-classics and Anomaly Matching
• The Resurgence of the Cusp Anomalous Dimension
• Orbifolds and Exact Solutions of Strongly-Coupled Matrix Models
• IR Renormalons vs. Operator Product Expansion in Supersymmetric and Related Gauge Theories
• Uniformization and Constructive Analytic Continuation of Taylor Series
• The curious incident of multi-instantons and the necessity of Lefschetz thimbles
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• Finite N from Resurgent Large N
• Lattice study on QCD-like theory with exact center symmetry
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• How to resum perturbative series in 3d N=2 Chern-Simons matter theories
• Relating 't Hooft Anomalies of 4d Pure Yang-Mills and 2d ${\mathbb{CP}}^{N-1}$ Model
• Relations among topological solitons
• Multi-flavor massless QED${}_2$ at finite densities via Lefschetz thimbles
• Complex structures and zero-curvature equations for sigma-models
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• 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
• Resurgence of the Renormalization Group Equation
• Topological solitons in the supersymmetric Skyrme model
• Flag manifold sigma models: spin chains and integrable theories
• Resurgence for superconductors
• New renormalons from analytic trans-series
• Generating a non-perturbative mass gap using Feynman diagrams in an asymptotically free theory
• On Perturbation theory improved by Strong coupling expansion
• The two-dimensional O(3) model at nonzero density: from dual lattice simulations to repulsive bosons
• Fractional instanton of the SU($3$) gauge theory in weak coupling regime
• Phase structure of the twisted $SU(3)/U(1{)}^2$ flag sigma model on $\mathbb{R}\times S^1$
• Gradient flows without blow-up for Lefschetz thimbles
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• Neutral bions in the CP^{N-1} model for resurgence
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• Josephson instantons and Josephson monopoles in a non-Abelian Josephson junction
• The SU(3)/Z_3 QCD(adj) deconfinement transition via the gauge theory/"affine" XY-model duality
• Nonlinear sigma models at nonzero chemical potential: breaking up instantons and the phase diagram
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• Bands and gaps in Nekrasov partition function
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• Adiabatic continuity and confinement in supersymmetric Yang-Mills theory on the lattice
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• Revisiting the Faddeev-Skyrme Model and Hopf Solitons
• Hydrodynamic Attractor in a Hubble Expansion
• Fractional Skyrmion molecules in a $\mathbb{C}{P}^{N-1}$ model
• Topology and $\theta$ dependence in finite temperature $G_2$ lattice gauge theory
• Quantum phase transition in many-flavor supersymmetric QED${}_3$
• Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles
• Renormalon structure in compactified spacetime
• Universal Renormalons in Principal Chiral Models
• Complex Path Integrals and the Space of Theories
• Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: ${\varphi }^3$ QFT in 6 Dimensions
• Lattice $\mathbb{C}{P}^{N-1}$ model with ${\mathbb{Z}}_N$ twisted boundary condition: bions, adiabatic continuity and pseudo-entropy
• Exponential reduction of finite volume effects with twisted boundary conditions
• Resurgence in the Bi-Yang-Baxter Model
• A new renormalon in two dimensions
• Clustering and decomposition for non BPS solutions of the ${\mathbb{CP}}^{N-1}$ models
• Resurgence of the QCD Adler function
• Instantons, renormalons and the theta angle in integrable sigma models
• Resurgence of a de Sitter Glauber-Sudarshan State: Nodal Diagrams and Borel Resummation
• Quantum distillation in QCD
• Resurgence in Lorentzian quantum cosmology: No-boundary saddles and resummation of quantum gravity corrections around tunneling saddle points
• Visions in Quantum Gravity
• Interpolating function and Stokes Phenomena
• Treating Divergent Perturbation Theory: Lessons from Exactly Solvable 2D Models at Large $N$
• SUSY breaking by nonperturbative dynamics in a matrix model for 2D type IIA superstrings
• Aspects of Perturbation theory in Quantum Mechanics: The BenderWu Mathematica package
• Tracy-Widom distribution as instanton sum of 2D IIA superstrings
• Local Neumann semitransparent layers: resummation, pair production and duality
• Resurgence and Lefschetz thimble in 3d N=2 supersymmetric Chern-Simons matter theories
• Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED
• Identification of perturbative ambiguity canceled against bion
• Resumming perturbative series in the presence of monopole bubbling effects
• Strongly coupled QFT dynamics via TQFT coupling
• Renormalons beyond the Borel plane
• Finite-Density Massless Two-Color QCD at Isospin Roberge-Weiss Point and 't Hooft Anomaly
• The absence of IR renormalons in gauge theories on ${\mathbb{R}}^3\times {\mathbb{S}}^1$ and what it means for resurgence
• The analytic structure of the fixed charge expansion
• Resurgent Analysis of Localizable Observables in Supersymmetric Gauge Theories
• Self-consistent Analytic Solutions in Twisted $\mathbb{C}{P}^{N-1}$ Model in the Large-$N$ Limit
• Renormalons in quantum mechanics
• Complex instantons in sigma models with chemical potential
• Towards Lefschetz thimbles in Sigma models, I
• Resurgent transseries $\&$ Dyson-Schwinger equations
• Reconstruction of spectra and an algorithm based on the theorems of Darboux and Puiseux
• High order perturbation theory for difference equations and Borel summability of quantum mirror curves
• Statistics of Feynman amplitudes in ${\varphi }^4$-theory
• Large-$N$ ${\mathbb{CP}}^{N-1}$ sigma model on a Euclidean torus: uniqueness and stability of the vacuum
• TQFT at work for IR-renormalons, resurgence and Lefschetz decomposition
• S-duality Improved Perturbation Theory in Compactified Type I / Heterotic String Theory
• One-point functions of non-SUSY operators at arbitrary genus in a matrix model for type IIA superstrings
• New and Old about Renormalons: in Memoriam Kolya Uraltsev
• Cluster expansion and resurgence in Polyakov model
• Analyticity domain of a Quantum Field Theory and Accelero-summation
• The CP(N-1) model on a Disc and Decay of a Non-Abelian String
• Image-processing the topological charge density in the CP(N-1) model
• Vacuum energy of the Bukhvostov-Lipatov model
• What if string theory has a de Sitter excited state?
• The QCD Adler function and the muon $g-2$ anomaly from renormalons
• Resurgence and semiclassical expansion in two-dimensional large-$N$ sigma models
• Winding theta and destructive interference of instantons
• Exact instanton transseries for quantum mechanics
• Asymptotics in an Asymptotic CFT
• Resurgent representation of the Adler function in the large-${\beta }_0$ approximation of QCD
• Confinement as Analytic Continuation Beyond Infinity
• Resurgence and Dynamics of O(N) and Grassmannian Sigma Models
• Twisted CP(N-1) instanton projectors and the N-level quantum density matrix
• Resurgence in 2-dimensional Yang-Mills and a genus altering deformation
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• Resurgence of one-point functions in a matrix model for 2D type IIA superstrings
• The Compactified Principal Chiral Model's Mass Gap
• All-order Resurgence from Complexified Path Integral in a Quantum Mechanical System with Integrability
• On instability of ground states in 2D CP(N-1) and O(N) models at large N
• Infrared renormalon in $SU(N)$ QCD(adj.) on ${\mathbb{R}}^3\times S^1$
• Vacuum energy of the supersymmetric $\mathbb{C}{P}^{N-1}$ model on $\mathbb{R}\times S^1$ in the $1/N$ expansion
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• Graded Hilbert spaces, quantum distillation and connecting SQCD to QCD
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• Semilocal Fractional Instantons
• Resurgence, a problem of missing exponential corrections in asymptotic expansions
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• Polyakov Model in 't Hooft flux background: A quantum mechanical reduction with memory
• Geometric QCD II: The Confining Twistor String and Meson Spectrum
• Nonperturbative features in the Lie-algebraic Kähler sigma model with fermions
• On Lagrangian description of Borel resummation