Pauli-Term-Induced Fixed Points in $d$-dimensional QED

TL;DR

This paper investigates how adding a Pauli spin-field coupling affects the fixed-point structure of QED-like theories across different dimensions and flavor numbers, revealing stability conditions and constructing RG trajectories relevant to condensed matter systems.

Contribution

It extends the understanding of fixed points in QED-like theories with Pauli coupling across various dimensions and flavor numbers, identifying stable fixed points and their implications.

Findings

Non-Gaussian fixed points destabilize with increasing dimensions and flavors.

A stable fixed point exists at finite Pauli coupling with zero gauge coupling.

Constructed RG trajectories connect fixed points to the QED3 universality class.

Abstract

We explore the fixed-point structure of QED-like theories upon the inclusion of a Pauli spin-field coupling. We concentrate on the fate of UV-stable fixed points recently discovered in $d=4$ spacetime dimensions upon generalizations to lower as well as higher dimensions for an arbitrary number of fermion flavors $N_\mathrm{f}$. As an overall trend, we observe that going away from $d=4$ dimensions and increasing the flavor number tends to destabilize the non-Gaussian fixed points discovered in four spacetime dimensions. A notable exception is a non-Gaussian fixed point at finite Pauli spin-field coupling but vanishing gauge coupling, which also remains stable down to $d=3$ dimensions and for small flavor numbers. This includes also the range of degrees of freedom used in effective theories of layered condensed-matter systems. As an application, we construct renormalization group trajectories that emanate from the non-Gaussian fixed point and approach a long-range regime in the conventional QED${}_3$ universality class that is governed by the interacting (quasi) fixed point in the gauge coupling.