Running coupling and non-perturbative corrections for O$(N)$ free energy and for disk capacitor

Abstract

We reconsider the complete solution of the linear TBA equation describing the energy density of finite density states in the $O(N)$ nonlinear sigma models by the Wiener-Hopf method. We keep all perturbative and non-perturbative contributions and introduce a running coupling in terms of which all asymptotic series appearing in the problem can be represented as pure power series without logs. We work out the first non-perturbative contribution in the $O(3)$ case and show that (presumably because of the instanton corrections) resurgence theory fails in this example. Using the relation of the $O(3)$ problem to the coaxial disks capacitor problem we work out the leading non-perturbative terms for the latter and show that (at least to this order) resurgence theory, in particular the median resummation prescription, gives the correct answer. We demonstrate this by comparing the Wiener-Hopf results to the high precision numerical solution of the original integral equation.

arXiv comment56 pages, 4 figures, LaTeX. v3: discussion of resurgence clarified, 1 reference added v4: eqs (4.29) and (4.30) corrected

References in corpus (19)

• Renormalons
• 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
• Compelling evidence of renormalons in QCD from high order perturbative expansions
• Scaling function in AdS/CFT from the O(6) sigma model
• Quantum integrability and functional equations
• From the mass gap in O(N) to the non-Borel-summability in O(3) and O(4) sigma-models
• Renormalons in integrable field theories
• Nonperturbative scales in AdS/CFT
• Resurgence in the O(4) sigma model
• The Exact Mass-Gap of the Supersymmetric CP^{n-1} Sigam Model
• The capacitance of the circular parallel plate capacitor obtained by solving the Love integral equation using an analytic expansion of the kernel
• The Exact Mass-Gap of the Supersymmetric O(N) Sigma Model
• 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
• Instanton effects vs resurgence in the $O(3)$ sigma model
• Analytical results for the capacitance of a circular plate capacitor

Cited by in corpus (2)

• Instantons, renormalons and the theta angle in integrable sigma models
• All-order Resurgence from Complexified Path Integral in a Quantum Mechanical System with Integrability