Universal Renormalons in Principal Chiral Models

Abstract

Perturbative expansions in many physical systems yield 'only' asymptotic series which are not even Borel resummable. Interestingly, the corresponding ambiguities point to nonperturbative physics. We numerically verify this renormalon mechanism for the first time in two-dimensional sigma models, that, like four-dimensional gauge theories, are asymptotically free and generate a strong scale through dimensional transmutation. We perturbatively expand the energy through a numerical version of stochastic quantization. In contrast to the first energy coefficients, the high order coefficients are independent on the rank of the model. Technically, they require a sophisticated analysis of finite volume effects and the continuum limit of the discretized model. Although the individual coefficients do not grow factorially (yet), but rather decrease strongly, the ratio of consecutive coefficients clearly obey the renormalon asymptotics.

Published version, updated references, minor text changes, 13 pages, 10 figures, REVTeX style

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Cited by in corpus (11)

• Renormalons in integrable field theories
• Resurgence in the O(4) sigma model
• New renormalons from analytic trans-series
• Testing the Bethe ansatz with large N renormalons
• Infrared renormalon in the supersymmetric $\mathbb{C}{P}^{N-1}$ model on $\mathbb{R}\times S^1$
• Resurgence and renormalons in the one-dimensional Hubbard model
• A new renormalon in two dimensions
• Treating Divergent Perturbation Theory: Lessons from Exactly Solvable 2D Models at Large $N$
• Confinement as Analytic Continuation Beyond Infinity
• Perturbative study of large $N$ principal chiral model with twisted reduction
• Lessons from $O(N)$ models in one dimension