Representation of Renormalization Group Functions By Nonsingular Integrals in a Model of the Critical Dynamics of Ferromagnets: The Fourth Order of The ε-Expansion

2018 ◽  
Vol 195 (1) ◽  
pp. 584-594 ◽  
Author(s):  
L. Ts. Adzhemyan ◽  
S. E. Vorob’eva ◽  
E. V. Ivanova ◽  
M. V. Kompaniets
Keyword(s):  
Renormalization Group ◽  
Fourth Order ◽  
Critical Dynamics ◽  
Group Functions

scholarly journals Six-dimensional ultraviolet completion of the ℂℙ(N) σ model at two loops

2020 ◽  
Vol 35 (22) ◽  
pp. 2050188
Author(s):  
J. A. Gracey
Keyword(s):  
Renormalization Group ◽  
Quantum Electrodynamics ◽  
Matter Field ◽  
Coupling Constants ◽  
Universal Theory ◽  
Gauge Parameter ◽  
Loop Analysis ◽  
Four Dimensions ◽  
Anomalous Dimensions ◽  
Group Functions

We extend the recent one-loop analysis of the ultraviolet completion of the [Formula: see text] nonlinear [Formula: see text] model in six dimensions to two-loop order in the [Formula: see text] scheme for an arbitrary covariant gauge. In particular we compute the anomalous dimensions of the fields and [Formula: see text]-functions of the four coupling constants. We note that like Quantum Electrodynamics (QED) in four dimensions the matter field anomalous dimension only depends on the gauge parameter at one loop. As a nontrivial check we verify that the critical exponents derived from these renormalization group functions at the Wilson–Fisher fixed point are consistent with the [Formula: see text] expansion of the respective large [Formula: see text] exponents of the underlying universal theory. Using the Ward–Takahashi identity we deduce the three-loop [Formula: see text] renormalization group functions for the six-dimensional ultraviolet completeness of scalar QED.

Sign in / Sign up

Export Citation Format

Share Document