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| As Contributors: | Slava Rychkov · Andreas Stergiou |
| Arxiv Link: | https://arxiv.org/abs/1810.10541v4 |
| Date accepted: | 2019-01-14 |
| Date submitted: | 2019-01-09 |
| Submitted by: | Stergiou, Andreas |
| Submitted to: | SciPost Physics |
| Domain(s): | Theoretical |
| Subject area: | High-Energy Physics - Theory |
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.
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.