Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 17 (2021), 075, 18 pages      arXiv:2011.13822      https://doi.org/10.3842/SIGMA.2021.075
Contribution to the Special Issue on Algebraic Structures in Perturbative Quantum Field Theory in honor of Dirk Kreimer for his 60th birthday

Resurgent Analysis of Ward-Schwinger-Dyson Equations

Marc P. Bellon and Enrico I. Russo
Sorbonne Université, CNRS, Laboratoire de Physique Théorique et Hautes Energies, Paris, France

Received February 10, 2021, in final form July 30, 2021; Published online August 11, 2021

Abstract
Building on our recent derivation of the Ward-Schwinger-Dyson equations for the cubic interaction model, we present here the first steps of their resurgent analysis. In our derivation of the WSD equations, we made sure that they had the properties of compatibility with the renormalisation group equations and independence from a regularisation procedure which was known to allow for the comparable studies in the Wess-Zumino model. The interactions between the transseries terms for the anomalous dimensions of the field and the vertex is at the origin of unexpected features, for which the effect of higher order corrections is not precisely known at this stage: we are only at the beginning of the journey to use resurgent methods to decipher non-perturbative effects in quantum field theory.

Key words: renormalization; Schwinger-Dyson equation; resurgence.

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