Seminarium "Teoria cząstek elementarnych i kosmologia"

In this talk, I will give an overview of Exact Renormalization Group techniques and apply them to the study of fixed points in Beyond the Standard Model (BSM) theories coupled to Quantum Gravity (QG). I will begin by motivating the need for non-perturbative physics and introducing the renormalization group idea proposed by Wilson. Structural differences between the Wilsonian proper-time and Wetterich flow equations will be highlighted, with the former being the main focus of the talk. Following Phys. Rev. D 113, 045020 (2026), I will discuss the perturbative structure of the proper-time renormalization group flow. Although the proper-time flow does not belong to the class of exact functional renormalization group equations, we show that it correctly reproduces the universal coefficients of the $\beta$-functions of $O(N)$ and Yang–Mills theories at one and two loops. I will highlight several attempts to compute these coefficients using the Wetterich equation and discuss the differences between the Wetterich approach and the proper-time flow equation. These results show that, despite its limitations in reconstructing the full effective action, the proper-time flow retains the essential universal content of renormalization, explaining its reliability in many applications. One of the main applications of non-perturbative techniques is the computation of fixed points in Quantum Gravity within the framework known as Asymptotic Safety. I will show how the presence of a fixed point in the running of QG couplings can generate a fixed point for BSM couplings, thereby providing insights into the values of BSM couplings at energy scales relevant for collider physics. Finally, I will apply the proper-time flow equation to the running of the simplest QG model, Einstein–Hilbert gravity, and study the gauge and regulator dependence of the fixed point of this theory when coupled to the Standard Model.