General applicability of parametric integration with hyperlogarithms to dynamic critical models

Determine the general applicability of the parametric integration method with Goncharov polylogarithms (HyperInt) to multiloop analytic calculations in models of critical dynamics, beyond exceptionally simple cases such as the high–spatial-dimension turbulence model where all diagrams are linearly reducible.

Background

The paper investigates whether modern analytic techniques—specifically parametric integration with hyperlogarithms—can be adapted to multiloop calculations in dynamic critical models, which are more complex than static models due to time dependence, non-standard propagators, and time-cut structures. A prior four-loop application to a turbulence model in the limit of high spatial dimension succeeded because all diagrams were linearly reducible without additional manipulations.

Motivated by this, the authors examine model A, a simple but nontrivial dynamic model, and encounter reducibility obstacles (notably diagram C9) that required developing a stream-based integration approach. This experience highlights that while the method can work in certain cases, its scope across dynamic models remains uncertain.