Singularities in the RG flow

TL;DR

This paper explores how certain operators in quantum field theories become relevant in the infrared due to IR singularities, specifically IR Landau poles, altering the expected behavior of the RG flow.

Contribution

It demonstrates that IR Landau poles can cause perturbatively irrelevant operators to become relevant, highlighting the role of infinite modes in the RG flow.

Findings

IR Landau poles induce relevance of operators in the IR

Four-fermion interactions can lead to bound state formation

Infinite modes in RG flow cause IR singularities

Abstract

In this work, we show examples when a perturbatively irrelevant operator becomes relevant in the infrared because of the presence of an IR singularity (IR Landau pole). An example of this behavior is the four-fermion interaction that allows the formation of bound states. The reason of the appearance of the IR Landau pole is not the singular loop as in the purely perturbative case, but the infinite number of modes appearing in the RG flow.