# General Properties of Multiscalar RG Flows in $d=4-\varepsilon$

### Submission summary

 As Contributors: Slava Rychkov · Andreas Stergiou 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 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.

### Ontology / Topics

See full Ontology or Topics database.

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.