Borel-Écalle resummation of a two-point function. (English) Zbl 1508.81941
Summary: We provide an overview of the tools and techniques of resurgence theory used in the Borel-Écalle resummation method, which we then apply to the massless Wess-Zumino model. Starting from already known results on the anomalous dimension of the Wess-Zumino model, we solve its renormalisation group equation for the two-point function in a space of formal series. We show that this solution is 1-Gevrey and that its Borel transform is resurgent. The Schwinger-Dyson equation of the model is then used to prove an asymptotic exponential bound for the Borel transformed two-point function on a star-shaped domain of a suitable ramified complex plane. This proves that the two-point function of the Wess-Zumino model is Borel-Écalle summable.
MSC:
| 81T17 | Renormalization group methods applied to problems in quantum field theory |
| 81T15 | Perturbative methods of renormalization applied to problems in quantum field theory |
| 81Q40 | Bethe-Salpeter and other integral equations arising in quantum theory |
| 30F99 | Riemann surfaces |
| 40G10 | Abel, Borel and power series methods |
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