Continuity and Resurgence: towards a continuum definition of the CP(N-1) model

Abstract

We introduce a non-perturbative continuum framework to study the dynamics of quantum field theory (QFT), applied here to the CP(N-1) model, using Ecalle's theory of resurgent trans-series, combined with the physical principle of continuity, in which spatial compactification and a Born-Oppenheimer approximation reduce QFT to quantum mechanics, while preventing all intervening rapid cross-overs or phase transitions. The reduced quantum mechanics contains the germ of all non-perturbative data, e.g., mass gap, of the QFT, all of which are calculable. For CP(N-1), the results obtained at arbitrary N are consistent with lattice and large-N results. These theories are perturbatively non-Borel summable and possess the elusive IR-renormalon singularities. The trans-series expansion, in which perturbative and non-perturbative effects are intertwined, encapsulates the multi-length-scale nature of the theory, and eliminates all perturbative and non-perturbative ambiguities under consistent analytic continuation of the coupling. We demonstrate the cancellation of the leading non-perturbative ambiguity in perturbation theory against the ambiguity in neutral bion amplitudes. This provides a weak-coupling interpretation of the IR-renormalon, and a theorem by Pham et al implies that the mass gap is a resurgent function, for which resummation of the semi-classical expansion yields finite exact results.

4 pages, 1 figure

References in corpus (6)

• 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
• Abelian duality, confinement, and chiral symmetry breaking in QCD(adj)
• Instanton constituents in the O(3) model at finite temperature
• Theta-vacuum and large N limit in CP^{N-1} sigma models

Cited by in corpus (105)

• Resurgence and Trans-series in Quantum Field Theory: The CP(N-1) Model
• A Primer on Resurgent Transseries and Their Asymptotics
• Uniform WKB, Multi-instantons, and Resurgent Trans-Series
• Generating Non-perturbative Physics from Perturbation Theory
• Nonperturbative Ambiguities and the Reality of Resurgent Transseries
• Resurgence in QFT: Unitons, Fractons and Renormalons in the Principal Chiral Model
• 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
• Resurgence and the Nekrasov-Shatashvili Limit: Connecting Weak and Strong Coupling in the Mathieu and Lam'e Systems
• Modified instanton sum in QCD and higher-groups
• Anomaly matching for phase diagram of massless ${\mathbb{Z}}_N$-QCD
• Resurgent Transseries and the Holomorphic Anomaly: Nonperturbative Closed Strings in Local CP2
• Vacuum structure of bifundamental gauge theories at finite topological angles
• Hydrodynamics, resurgence and trans-asymptotics
• Complexified path integrals, exact saddles and supersymmetry
• The Resurgence of Instantons: Multi-Cut Stokes Phases and the Painleve II Equation
• Hidden topological angles and Lefschetz thimbles
• Neutral bions in the $\mathbb{C}{P}^{N-1}$ model
• Cheshire Cat resurgence, Self-resurgence and Quasi-Exact Solvable Systems
• Deconstructing zero: resurgence, supersymmetry and complex saddles
• Adjoint QCD on ${\mathbb{R}}^3\times S^1$ with twisted fermionic boundary conditions
• Non-perturbative Contributions from Complexified Solutions in $\mathbb{C}{P}^{N-1}$ Models
• 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
• Chiral Lagrangian from Duality and Monopole Operators in Compactified QCD
• Classifying bions in Grassmann sigma models and non-Abelian gauge theories by D-branes
• Phase diagram of Yang-Mills theories in the presence of a theta term
• Bion non-perturbative contributions versus infrared renormalons in two-dimensional $\mathbb{C}{P}^{N-1}$ models
• (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
• Resurgence in $\eta$-deformed Principal Chiral Models
• Quantum Distillation of Hilbert Spaces, Semi-classics and Anomaly Matching
• The Resurgence of the Cusp Anomalous Dimension
• IR Renormalons vs. Operator Product Expansion in Supersymmetric and Related Gauge Theories
• Fractional instantons and bions in the O(N) model with twisted boundary conditions
• Finite N from Resurgent Large N
• Remark on the Dunne-Unsal relation in exact semi-classics
• Relating 't Hooft Anomalies of 4d Pure Yang-Mills and 2d ${\mathbb{CP}}^{N-1}$ Model
• Relations among topological solitons
• 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
• Resurgence and Holomorphy: From Weak to Strong Coupling
• Topological solitons in the supersymmetric Skyrme model
• Flag manifold sigma models: spin chains and integrable theories
• On Perturbation theory improved by Strong coupling expansion
• Resurgence, Operator Product Expansion, and Remarks on Renormalons in Supersymmetric Yang-Mills
• Phase structure of the twisted $SU(3)/U(1{)}^2$ flag sigma model on $\mathbb{R}\times S^1$
• Instantons in Chiral Magnets
• Fractional instanton of the SU($3$) gauge theory in weak coupling regime
• The energy-momentum tensor and D-term of Q-clouds
• What is QFT? Resurgent trans-series, Lefschetz thimbles, and new exact saddles
• Creation of Magnetic Monopoles in Classical Scattering
• Josephson instantons and Josephson monopoles in a non-Abelian Josephson junction
• Fractionalized Non-Self-Dual Solutions in the CP(N-1) Model
• Infrared renormalon in the supersymmetric $\mathbb{C}{P}^{N-1}$ model on $\mathbb{R}\times S^1$
• Confinement-Deconfinement Crossover in the Lattice $\mathbb{C}{P}^{N-1}$ Model
• Revisiting the Faddeev-Skyrme Model and Hopf Solitons
• Fractional Skyrmion molecules in a $\mathbb{C}{P}^{N-1}$ model
• 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
• Exponential reduction of finite volume effects with twisted boundary conditions
• Lattice $\mathbb{C}{P}^{N-1}$ model with ${\mathbb{Z}}_N$ twisted boundary condition: bions, adiabatic continuity and pseudo-entropy
• Clustering and decomposition for non BPS solutions of the ${\mathbb{CP}}^{N-1}$ models
• Resurgence in Lorentzian quantum cosmology: No-boundary saddles and resummation of quantum gravity corrections around tunneling saddle points
• Interpolating function and Stokes Phenomena
• Treating Divergent Perturbation Theory: Lessons from Exactly Solvable 2D Models at Large $N$
• Identification of perturbative ambiguity canceled against bion
• 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
• Resumming perturbative series in the presence of monopole bubbling effects
• 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
• Resurgent transseries $\&$ Dyson-Schwinger equations
• Complex instantons in sigma models with chemical potential
• The analytic structure of the fixed charge expansion
• Resurgent Analysis of Localizable Observables in Supersymmetric Gauge Theories
• TQFT at work for IR-renormalons, resurgence and Lefschetz decomposition
• The CP(N-1) model on a Disc and Decay of a Non-Abelian String
• Winding theta and destructive interference of instantons
• Confinement as Analytic Continuation Beyond Infinity
• Resurgence and semiclassical expansion in two-dimensional large-$N$ sigma models
• Resurgence and Dynamics of O(N) and Grassmannian Sigma Models
• All-order Resurgence from Complexified Path Integral in a Quantum Mechanical System with Integrability
• Vacuum energy of the supersymmetric $\mathbb{C}{P}^{N-1}$ model on $\mathbb{R}\times S^1$ in the $1/N$ expansion
• Resurgence of one-point functions in a matrix model for 2D type IIA superstrings
• Twisted CP(N-1) instanton projectors and the N-level quantum density matrix
• Infrared renormalon in $SU(N)$ QCD(adj.) on ${\mathbb{R}}^3\times S^1$
• The Compactified Principal Chiral Model's Mass Gap
• Graded Hilbert spaces, quantum distillation and connecting SQCD to QCD
• More on the infrared renormalon in $SU(N)$ QCD(adj.) on ${\mathbb{R}}^3\times S^1$
• 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
• Yang-Mills at Strong vs. Weak Coupling: Renormalons, OPE And All That
• Resurgence in the Scalar Quantum Electrodynamics Euler-Heisenberg Lagrangian
• Polyakov Model in 't Hooft flux background: A quantum mechanical reduction with memory