# Universal Renormalons in Principal Chiral Models

## TL;DR

This paper numerically verifies the presence of renormalons in two-dimensional sigma models, demonstrating their role in nonperturbative physics and asymptotic series behavior similar to gauge theories.

## Contribution

First numerical verification of renormalon effects in 2D sigma models, linking perturbative ambiguities to nonperturbative phenomena in these models.

## Key findings

- High order coefficients are independent of model rank.
- Ratios of consecutive coefficients follow renormalon asymptotics.
- Individual coefficients decrease strongly, yet renormalon behavior is evident.

## 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.