Resurgence analysis of the Adler function at O $$ \mathcal{O} $$ (1/ N f 2 $$ {N}_f^2 $$ )

Abstract

Abstract 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/N f , 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/N f . We compute 3-loop planar diagrams, at order 1/ N f 2 $$ {N}_f^2 $$ , 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.

Keywords

• Large-Order Behaviour of Perturbation Theory
• Renormalons
• Nonperturbative Effects