# Bifurcations in the RG-flow of QCD

## TL;DR

This paper uses bifurcation analysis on an effective QCD model with four-fermi interactions to explore fixed points, scaling behaviors, and phase transitions within the conformal window, including effects of adding scalar fields.

## Contribution

It introduces a bifurcation analysis approach to study RG flows in an effective QCD model, revealing fixed point mergers, scaling laws, and the impact of scalar couplings.

## Key findings

- Support for fixed point merger at the conformal window edge
- Prediction of new fixed points and their transitions
- Exotic spiraling RG flows from complex scaling dimensions

## Abstract

Bifurcation analysis is used to study an effective model of QCD$_4$ with four-fermi interactions. Our analysis supports the scenario of a fixed point merger at the lower edge of the conformal window. This indicates square root scaling of the anomalous scaling dimensions of the fermion fields just above the lower edge and exponential scaling just below. We also predict existence of new fixed points in this model whose (dis)appearance may indicate transitions of the flow within the conformal window. Furthermore, we make new predictions for the critical value $(N_{f}/N_{c})_{\textrm{crit}}$ at the lower edge. We also obtain exotic spiraling flows that are generated by complex scaling dimensions of the effective four-fermi interactions. Finally, we extend the model by adding a scalar field that couples with a Yukawa interaction term and study the modifications it causes to RG-flows.