Analytic resurgence in the O(4) model

Abstract

We study the perturbative expansion of the ground state energy in the presence of an external field coupled to a conserved charge in the integrable two-dimensional O$(4)$ nonlinear sigma model. By solving Volin's algebraic equations for the perturbative coefficients we study the large order asymptotic behaviour of the perturbative series analytically. We confirm the previously numerically found leading behaviour and study the nearest singularities of the Borel transformed series and the associated alien derivatives. We find a 'resurgence' behaviour: the leading alien derivatives can be expressed in terms of the original perturbative series. A simplified 'toy' model is also considered: here the perturbative series can be found in a closed form and the resurgence properties are very similar to that found in the real problem.

arXiv comment35 pages, LaTeX, no figures

References in corpus (26)

• Renormalons
• Lectures on non-perturbative effects in large N gauge theories, matrix models and strings
• A Primer on Resurgent Transseries and Their Asymptotics
• An Introduction to Resurgence, Trans-Series and Alien Calculus
• Nonperturbative Ambiguities and the Reality of Resurgent Transseries
• New Methods in QFT and QCD: From Large-N Orbifold Equivalence to Bions and Resurgence
• Resurgence in Extended Hydrodynamics
• Compelling evidence of renormalons in QCD from high order perturbative expansions
• Scaling function in AdS/CFT from the O(6) sigma model
• $\lambda {\varphi }^4$ Theory I: The Symmetric Phase Beyond NNNNNNNNLO
• Bion non-perturbative contributions versus infrared renormalons in two-dimensional $\mathbb{C}{P}^{N-1}$ models
• Quantum integrability and functional equations
• 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
• Resurgence of the Cusp Anomalous Dimension
• The large proper-time expansion of Yang-Mills plasma as a resurgent transseries
• Resurgence in $\eta$-deformed Principal Chiral Models
• The Resurgence of the Cusp Anomalous Dimension
• Renormalons in integrable field theories
• $\lambda {\varphi }^4$ Theory II: The Broken Phase Beyond NNNN(NNNN)LO
• Resurgence in the O(4) sigma model
• New renormalons from analytic trans-series
• From perturbative to non-perturbative in the O(4) sigma model
• Resurgence of the dressing phase for ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$
• Testing the Bethe ansatz with large N renormalons
• Resurgence and renormalons in the one-dimensional Hubbard model

Cited by in corpus (10)

• Existence of real time quantum path integrals
• The full analytic trans-series in integrable field theories
• Renormalon cancellation and linear power correction to threshold-like asymptotics of space-like parton correlators
• Instantons, renormalons and the theta angle in integrable sigma models
• Running coupling and non-perturbative corrections for O$(N)$ free energy and for disk capacitor
• Resurgence and semiclassical expansion in two-dimensional large-$N$ sigma models
• Asymptotics in an Asymptotic CFT
• All-order Resurgence from Complexified Path Integral in a Quantum Mechanical System with Integrability
• Resurgence in the Scalar Quantum Electrodynamics Euler-Heisenberg Lagrangian
• Asymptotics in the bi-Yang-Baxter Sigma Model