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

by Slava Rychkov, Andreas Stergiou

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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