# 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 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.

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