Asymptotics in an Asymptotic CFT

Abstract

In this work we illustrate the resurgent structure of the $\lambda$-deformation; a two-dimensional integrable quantum field theory that has an RG flow with an $SU(N{)}_k$ Wess-Zumino-Witten conformal fixed point in the UV. To do so we use modern matched asymptotic techniques applied to the thermodynamic Bethe ansatz formulation to compute the free energy to 38 perturbative orders in an expansion of large applied chemical potential. We find numerical evidence for factorial asymptotic behaviour with both alternating and non-alternating character which we match to an analytic expression. A curiosity of the system is that it exhibits the Cheshire Cat phenomenon with the leading non-alternating factorial growth vanishing when $k$ divides $N$. The ambiguities associated to Borel resummation of this series are suggestive of non-perturbative contributions. This is verified with an analytic study of the TBA system demonstrating a cancellation between perturbative and non-perturbative ambiguities.

arXiv comment26 Pages, 7 figures

References in corpus (44)

• Integrable interpolations: From exact CFTs to non-Abelian T-duals
• Resurgence and Trans-series in Quantum Field Theory: The CP(N-1) Model
• A Primer on Resurgent Transseries and Their Asymptotics
• On integrable deformations of superstring sigma models related to AdS_n x S^n supercosets
• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• Multi-Instantons and Exact Results I: Conjectures, WKB Expansions, and Instanton Interactions
• An Integrable Deformation of the AdS5 x S5 Superstring
• Generalised integrable $\lambda$- and $\eta$-deformations and their relation
• $\eta$ and $\lambda$ deformations as $\mathcal{E}$-models
• Deformed integrable $\sigma$-models, classical $R$-matrices and classical exchange algebra on Drinfel'd doubles
• Integrable Deformations of Strings on Symmetric Spaces
• Resurgence in QFT: Unitons, Fractons and Renormalons in the Principal Chiral Model
• Spacetimes for λ-deformations
• Multi-Instantons and Exact Results II: Specific Cases, Higher-Order Effects, and Numerical Calculations
• Marginal Deformations of WZNW and Coset Models from O(d,d) Transformation
• Gauged WZW models and Non-abelian duality
• Beta Function of k Deformed AdS_5 x S^5 String Theory
• A new family of $SU(2)$ symmetric integrable sigma models
• Cheshire Cat resurgence, Self-resurgence and Quasi-Exact Solvable Systems
• Gauged WZW-type theories and the all-loop anisotropic non-Abelian Thirring model
• Poisson-Lie T-duals of the bi-Yang-Baxter models
• Quantum integrability and functional equations
• On a `universal' class of WZW-type conformal models
• The grin of Cheshire cat resurgence from supersymmetric localization
• From the mass gap in O(N) to the non-Borel-summability in O(3) and O(4) sigma-models
• The classical Yang-Baxter equation and the associated Yangian symmetry of gauged WZW-type theories
• Integrable theories that are asymptotically CFT
• Resurgence in $\eta$-deformed Principal Chiral Models
• Renormalons in integrable field theories
• S-Matrices and Quantum Group Symmetry of k-Deformed Sigma Models
• The exact mass-gaps of the principal chiral models
• New renormalons from analytic trans-series
• Resurgence for superconductors
• From perturbative to non-perturbative in the O(4) sigma model
• Testing the Bethe ansatz with large N renormalons
• Analytic resurgence in the O(4) model
• Picard-Lefschetz decomposition and Cheshire Cat resurgence in 3D $\mathcal{N}=2$ field theories
• Instanton effects vs resurgence in the $O(3)$ sigma model
• Quantum Inverse Scattering and the Lambda Deformed Principal Chiral Model
• Quantum Anisotropic Sigma and Lambda Models as Spin Chains
• Resurgence in the Bi-Yang-Baxter Model
• Strong integrability of $\lambda$-deformed models
• A new renormalon in two dimensions
• OPE coefficients and the mass-gap from the integrable scattering description of 2D CFT's

Cited by in corpus (2)

• Trans-series from condensates
• Asymptotics in the bi-Yang-Baxter Sigma Model