New renormalons from analytic trans-series

Abstract

We study the free energy of integrable, asymptotically free field theories in two dimensions coupled to a conserved charge. We develop methods to obtain analytic expressions for its trans-series expansion, directly from the Bethe ansatz equations, and we use this result to determine the structure of its Borel singularities. We find a new class of infrared renormalons which does not fit the traditional expectations of renormalon physics proposed long ago by 't Hooft and Parisi. We check the existence of these new singularities with detailed calculations based on the resurgent analysis of the perturbative expansion. Our results show that the structure of renormalons in asymptotically free theories is more subtle than previously thought, and that large $N$ estimates of their location might be misleading.

58 pages, 17 figures - v4: corrected the discussion of the instanton-like contributions in the PCF model

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Cited by in corpus (13)

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• Analytic resurgence in the O(4) model
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• Resurgence in Lorentzian quantum cosmology: No-boundary saddles and resummation of quantum gravity corrections around tunneling saddle points
• Asymptotics in an Asymptotic CFT
• Exploring superconformal Yang-Mills theories through matrix Bessel kernels
• All-order Resurgence from Complexified Path Integral in a Quantum Mechanical System with Integrability
• Trans-series from condensates
• Condensates, crystals, and renormalons in the Gross-Neveu model at finite density
• Asymptotics in the bi-Yang-Baxter Sigma Model
• Nonperturbative features in the Lie-algebraic Kähler sigma model with fermions
• Trans-series from condensates in the non-linear sigma model