Abstract
We investigate the renormalization group flows of multicomponent scalar theories with gauge symmetry using the functional renormalization group method. The scalar sector is built up from traces of matrix fields that belong to simple, compact Lie algebras. We find that in these theories the local potential approximation (LPA) is not a one-loop closed truncation in general, even at zero gauge coupling. If, however, we add a factor to the Lie algebra structure, then the LPA always becomes one-loop closed. In accordance with our earlier findings, fluctuations introduce anomalous, regulator dependent gauge contributions, which are only consistent with the flow equation for a given set of gauge fixing parameters. We establish connections between regularization procedures in the standard covariant and the gauges arguing that one is not tied by introducing regulators at the level of the functional integral, and it is allowed to switch between schemes at different levels of the calculations. We calculate functions, classify fixed points, and clarify compatibility of the flow equation and the Ward-Takahashi identity between the scalar wave function renormalization and the charge rescaling factor.
- Received 22 May 2019
DOI:https://doi.org/10.1103/PhysRevD.100.036007
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
Published by the American Physical Society