Abstract
This work investigates the fixed points and the stability properties of the corresponding scalar potentials of Gauge-Yukawa theories nonperturbatively using Functional Renormalization Group (FRG), in particular the Wetterich Equation. The Gauge-Yukawa theories contain gauge fields, fermions and matrix-valued scalar fields. The theories develop an interacting ultraviolet fixed point making the theories asymptotically safe. Moreover, they are perturbatively accessible in a particular limit, the Veneziano limit. The work introduces basic concepts of FRG and Asymptotic Safety. It summarizes the perturbative results for the Gauge-Yukawa theories and works out the nonperturbative equations following from Wetterich's equation. Various methods to solve FRG equations are described in detail. Moreover, the fixed-point landscape with their corresponding fixed-point potentials and stability porperties is calculated together with the critical exponents of the theory at the fixed points.
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