The a-function in six dimensions
J.A. Gracey, I. Jack, C. Poole
TL;DR
This paper investigates the properties of the a-function in six-dimensional scalar theories, analyzing its behavior along renormalization group flows using advanced three-loop beta-function calculations in multiple schemes.
Contribution
It provides the first three-loop beta-function calculations in the MOM scheme for six-dimensional scalar theories and explores the a-function's monotonicity in this context.
Findings
First three-loop beta-functions in MOM scheme for six dimensions
Evidence supporting the a-function's monotonic behavior in six dimensions
Comparison between MSbar and MOM scheme results
Abstract
The a-function is a proposed quantity defined in even dimensions which has a monotonic behaviour along RG flows, related to the beta-functions via a gradient flow equation. We study the a-function for a general scalar theory in six dimensions, using the beta-functions up to three-loop order for both the MSbar and MOM schemes (the latter presented here for the first time at three loops).
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