2019/12/06 by Pierre J. Clavier, Clavier, Pierre J.
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1912.03237
25 pages, clarifications and precisions added. Expanded discussion of the physical consequences of this work. Typos removed and grammatical mistakes fixed. Bibliography updated and completed. To be published in Annales Henri Poincaré
arxiv created 2021/04/21 · arxiv updated 2021/04/22
We provide an overview of the tools and techniques of resurgence theory used in the Borel-Ecalle 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 prove that the two point function of the Wess-Zumino model is Borel-Ecalle summable.