Testing the Bethe ansatz with large N renormalons

Abstract

The ground state energy of integrable asymptotically free theories can be conjecturally computed by using the Bethe ansatz, once the theory has been coupled to an external potential through a conserved charge. This leads to a precise prediction for the perturbative expansion of the energy. We provide a non-trivial test of this prediction in the non-linear sigma model and its supersymmetric extension, by calculating analytically the associated Feynman diagrams at next-to-leading order in the $1/N$ expansion, and at all loops. By investigating the large order behaviour of the diagrams, we locate the position of the renormalons of the theory and we obtain an analytic expression for the large $N$ trans-series associated to each. As a spin-off of our calculation, we provide a direct derivation of the beta function of these theories, at next-to-leading order in the $1/N$ expansion.

arXiv comment39 pages, 8 figures

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Cited by in corpus (14)

• New renormalons from analytic trans-series
• The full analytic trans-series in integrable field theories
• Renormalon cancellation and linear power correction to threshold-like asymptotics of space-like parton correlators
• Analytic resurgence in the O(4) model
• Instantons, renormalons and the theta angle in integrable sigma models
• Resurgence in Lorentzian quantum cosmology: No-boundary saddles and resummation of quantum gravity corrections around tunneling saddle points
• Running coupling and non-perturbative corrections for O$(N)$ free energy and for disk capacitor
• Cluster expansion and resurgence in Polyakov model
• Asymptotics in an Asymptotic CFT
• All-order Resurgence from Complexified Path Integral in a Quantum Mechanical System with Integrability
• Asymptotics in the bi-Yang-Baxter Sigma Model
• Renormalon-like factorial enhancements to power expansion/OPE in a super-renormalizable 2D $O(N)$ quartic model
• Nonperturbative features in the Lie-algebraic Kähler sigma model with fermions
• Trans-series from condensates in the non-linear sigma model