SciPost Submission Page
General Properties of Multiscalar RG Flows in $d=4-\varepsilon$
by Slava Rychkov, Andreas Stergiou
This Submission thread is now published as
Submission summary
| Submission information |
| Arxiv Link: |
https://arxiv.org/abs/1810.10541v4 (pdf)
|
| Date accepted: |
2019-01-14 |
| Date submitted: |
2019-01-09 01:00 |
| Submitted by: |
Stergiou, Andreas |
| Submitted to: |
SciPost Physics |
| Ontological classification |
| Academic field: |
Physics |
| Specialties: |
- Condensed Matter Physics - Theory
- High-Energy Physics - Theory
|
| Approach: |
Theoretical |
Abstract
Fixed points of scalar field theories with quartic interactions in
$d=4-\varepsilon$ dimensions are considered in full generality. For such
theories it is known that there exists a scalar function $A$ of the couplings
through which the leading-order beta-function can be expressed as a gradient.
It is here proved that the fixed-point value of $A$ is bounded from below by a
simple expression linear in the dimension of the vector order parameter, $N$.
Saturation of the bound requires a marginal deformation, and is shown to arise
when fixed points with the same global symmetry coincide in coupling space.
Several general results about scalar CFTs are discussed, and a review of known
fixed points is given.
Published as
SciPost Phys. 6, 008 (2019)
Author comments upon resubmission
We would like to thank the referees for the careful reading of our manuscript. As suggested by Report 1, we rescaled B away earlier in the manuscript, and fixed footnote 3. We also added a few comments about next-to-leading order results in the conclusion, specifically around eq. (7.7), and footnote 20.
