2023/02/27 by Eric Laenen, Laenen, Eric, Coenraad Marinissen +3
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2302.13715
openalex publication_date 2023/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We compute non-perturbative contributions to the Adler function, the derivative of the vacuum polarization function in gauge theory, using resurgence methods and Borel-summed gauge field propagators. At 2-loop, to order 1/Nf, we construct the full 2-parameter transseries and perform the sum over the non-perturbative sectors. We then introduce a convolution-based method to derive the transseries structure of product series, which can also be used to study higher orders in the expansion in 1/Nf. We compute 3-loop planar diagrams, at order 1/Nf2, and for each diagram study the asymptotic behavior and resulting non-perturbative information in the transseries. A structure emerges that, from a resurgence point of view, is quite different from toy models hitherto studied. We study in particular the first and second non-perturbative sectors, their relation to UV and IR renormalons, and how their presence influences the perturbative expansions in neighbouring sectors. Finally, finding that many non-perturbative sectors have asymptotic series, we derive relations among all of them, thus providing an interesting new perspective on the alien lattice for the Adler function.