The analytic structure of the fixed charge expansion

Abstract

We investigate the analytic properties of the fixed charge expansion for a number of conformal field theories in different space-time dimensions. The models investigated here are $O(N)$ and $QE{D}_3$. We show that in $d=3-\epsilon$ dimensions the contribution to the $O(N)$ fixed charge $Q$ conformal dimensions obtained in the double scaling limit of large charge and vanishing $\epsilon$ is non-Borel summable, doubly factorial divergent, and with order $\sqrt{Q}$ optimal truncation order. By using resurgence techniques we show that the singularities in the Borel plane are related to worldline instantons that were discovered in the other double scaling limit of large $Q$ and $N$ of Ref. [1]. In $d=4-\epsilon$ dimensions the story changes since in the same large $Q$ and small $\epsilon$ regime the next order corrections to the scaling dimensions lead to a convergent series. The resummed series displays a new branch cut singularity which is relevant for the stability of the $O(N)$ large charge sector for negative $\epsilon$. Although the $QE{D}_3$ model shares the same large charge behaviour of the $O(N)$ model, we discover that at leading order in the large number of matter field expansion the large charge scaling dimensions are Borel summable, single factorial divergent, and with order $Q$ optimal truncation order.

arXiv comment24 pages, 4 figures, 1 table

References in corpus (61)

• Quantum Field Theory in the Large N Limit: a review
• Perturbative Quantum Field Theory in the String-Inspired Formalism
• Topological Disorder Operators in Three-Dimensional Conformal Field Theory
• Resurgence and Trans-series in Quantum Field Theory: The CP(N-1) Model
• A Primer on Resurgent Transseries and Their Asymptotics
• An Introduction to Resurgence, Trans-Series and Alien Calculus
• The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
• Confinement and complex singularities in QED3
• Spin correlations in the algebraic spin liquid - implications for high Tc superconductors
• Semiclassics, Goldstone Bosons and CFT data
• A semiclassical realization of infrared renormalons
• Compensating strong coupling with large charge
• Continuity and Resurgence: towards a continuum definition of the CP(N-1) model
• The Epsilon Expansion Meets Semiclassics
• Higher Spin AdS${}_{d+1}$/CFT${}_d$ at One Loop
• QCD Critical Point and Complex Chemical Potential Singularities
• Structure of Lefschetz thimbles in simple fermionic systems
• Towards Bootstrapping QED${}_3$
• Hidden topological angles and Lefschetz thimbles
• Semiclassical approach for multiparticle production in scalar theories
• On the Large $R$-charge Expansion in $\mathcal{N}=2$ Superconformal Field Theories
• Physical Resurgent Extrapolation
• Large charge at large N
• From 4d Yang-Mills to 2d ${\mathbb{CP}}^{N-1}$ model: IR problem and confinement at weak coupling
• Feynman diagrams and the large charge expansion in $3-\epsilon$ dimensions
• Hyperasymptotics and quark-hadron duality violations in QCD
• On the role of power expansions in quantum field theory
• Complex Saddles in Two-dimensional Gauge Theory
• The large charge limit of scalar field theories and the Wilson-Fisher fixed point at $\epsilon =0$
• Resurgence of the Cusp Anomalous Dimension
• Non-Perturbative Completion of Hopf-Algebraic Dyson-Schwinger Equations
• Bootstrapping $N_f=4$ conformal QED${}_3$
• Renormalons in integrable field theories
• A note on the large charge expansion in 4d CFT
• A safe CFT at large charge
• The large charge expansion at large N
• Resurgence of the large-charge expansion
• Resurgence in the O(4) sigma model
• Near-Conformal Dynamics at Large Charge
• Resurgence of the Renormalization Group Equation
• On the Higher Loop Euler-Heisenberg Trans-Series Structure
• More on the Weak Gravity Conjecture via Convexity of Charged Operators
• Transmutation of a Trans-series: The Gross-Witten-Wadia Phase Transition
• Anomalous dimensions for ${\varphi }^n$ in scale invariant $d=3$ theory
• Untangling scaling dimensions of fixed charge operators in Higgs Theories
• Series extension: Predicting approximate series coefficients from a finite number of exact coefficients
• The OPE meets semiclassics
• Anomalous dimensions at large charge in d=4 O(N) theory
• More on the cubic versus quartic interaction equivalence in the $O(N)$ model
• Towards the QED beta function and renormalons at $1/N_f^2$ and $1/N_f^3$
• Analytic Coupling Structure of Large $N_f$ (Super) QED and QCD
• Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: Matrix Model and Classical String
• Uniformizing Lee-Yang Singularities
• Nonrelativistic CFTs at Large Charge: Casimir Energy and Logarithmic Enhancements
• Instantons or Renormalons? A Comment on phi4_4 Theory in the MS Scheme
• Anomalous dimensions at large charge for $U(N)\times U(N)$ theory in three and four dimensions
• Following the flow for large N and large charge
• Resurgence of the QCD Adler function
• Sub-leading conformal dimensions at the O(4) Wilson-Fisher fixed point
• Boundary Conformal Field Theory at Large Charge
• Critical number of fermions in three-dimensional QED

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