## SciPost Submission Page

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

### by Slava Rychkov, Andreas Stergiou

####
- Published as
SciPost Phys.
**6**,
8
(2019)

### Submission summary

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 |

### 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.

###### Current status:

**6**, 8 (2019)

### Ontology / Topics

See full Ontology or Topics database.### 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.