Pauli-term-induced fixed points in d-dimensional QED

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\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d=4$$\\end{document} spacetime dimensions upon generalizations to lower as well as higher dimensions for an arbitrary number of fermion flavors Nf.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_{\ ext {f}}.$$\\end{document} As an overall trend, we observe that going away from d=4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d=4$$\\end{document} 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\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d=3$$\\end{document} 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 QED3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}_3$$\\end{document} universality class that is governed by the interacting (quasi) fixed point in the gauge coupling.