Bifurcations in the RG-flow of QCD

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 $(N_f/N_c{)}_{\text{crit}}$ 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.

arXiv comment31+26 pages; references added, typos corrected

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Cited by in corpus (6)

• Conformal window from conformal expansion
• Looking through the QCD Conformal Window with Perturbation Theory
• Homoclinic RG flows, or when relevant operators become irrelevant
• Spectral Functions of Gauge Theories with Banks-Zaks Fixed Points
• Continuous order-to-order quantum phase transitions from fixed-point annihilation
• Conformal Windows beyond Asymptotic Freedom