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Résumé |
Understanding the behavior of perturbative series in quantum field theory is an old
and venerable problem. In the 1970s-1980s it was found that this behavior is closely connected to
non-perturbative physics, and ’t Hooft and Parisi argued that the most important non-perturbative
corrections in
asymptotically free theories are due to so-called renormalons. In contrast to instantons, renormalons do not
have a semi-classical description, they are difficult to compute, and they are still poorly understood.
In this talk I will first summarize what is known about the physics and mathematics of renormalons.
I will then argue that integrable field theories in two dimensions provide an excellent laboratory to
obtain analytic results on the structure or renormalons. Some of these exact results turn out to challenge the
standard
orthodoxy on the subject. I will also explain how renormalons provide "trans-series”
representations for observables, i.e. extensions of perturbation theory which include exponentially small
corrections, as expected f rom the theory of resurgence. |
