e-Article
Explorations in scalar fermion theories: $\beta $-functions, supersymmetry and fixed points.
Document Type
Journal
Author
Jack, Ian (4-LVRP) AMS Author Profile; Osborn, Hugh (4-CAMB-A) AMS Author Profile; Steudtner, Tom (D-DTUP) AMS Author Profile
Source
Subject
81 Quantum theory -- 81T Quantum field theory; related classical field theories
81T15Perturbative methods of renormalization
81T17Renormalization group methods
81T60Supersymmetric field theories
81T15
81T17
81T60
Language
English
Abstract
Summary: ``Results for $\beta$-functions and anomalous dimensions in general scalar fermion theories are presented to three loops. Various constraints on the individual coefficients for each diagram following from supersymmetry are analysed. The results are used to discuss potential fixed points in the $\varepsilon$-expansion for scalar fermion theories, with arbitrary numbers of scalar fields, and where there are just two scalar couplings and one Yukawa coupling. For different examples the fixed points follow a similar pattern as the numbers of fermions is varied. For diagrams with subdivergences there are extensive consistency constraints arising from the existence of a perturbative a-function and these are analysed in detail. Further arbitrary scheme variations which preserve the form of $\beta$ functions and anomalous dimensions in terms of 1PI diagrams are also discussed. The existence of linear and quadratic scheme invariants is demonstrated and the consistency condition are shown to be expressible in terms of these invariants.''