Speaker
Description
This talk presents the application of parametric integration with Goncharov polylogarithms to multiloop analytic calculations in models of critical dynamics. The technique has been successfully applied in various high-energy physics and static critical models. Its main requirement is linear reducibility of the integrals under evaluation. In dynamical models, linearly non-reducible integrals already appear at low-loop orders and their analytic structure differs from that in static models.
We discuss the application of the parametric integration in the model of stochastic turbulence in the $d\to\infty$ limit and the model A based on $\phi^4$-theory, both in the four-loop approximation. Also, the model A based on $\phi^3$-theory is considered, where the two-loop order is obtained analytically. We propose a method to evaluate linearly non-reducible dynamical integrals based on splitting the integrand into separately reducible streams. The approach can be applied to diagrams in any model, where standard techniques, such as changes of variables, fail to restore reducibility.
