## General properties of multiscalar RG Flows in $d=4-\varepsilon$

Slava Rychkov, Andreas Stergiou

SciPost Phys. 6, 008 (2019) · published 17 January 2019

- doi: 10.21468/SciPostPhys.6.1.008
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### 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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### Ontology / Topics

See full Ontology or Topics database.### Authors / Affiliations: mappings to Contributors and Organizations

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^{1 }^{2 }Slava Rychkov, -
^{3 }^{4 }Andreas Stergiou

^{1}Institut des Hautes Études Scientifiques [IHÉS]^{2}École Normale Supérieure [ENS]^{3}Los Alamos National Laboratory [LANL]^{4}Organisation européenne pour la recherche nucléaire / European Organization for Nuclear Research [CERN]

- Engineering and Physical Sciences Research Council [EPSRC]
- Isaac Newton Institute for Mathematical Sciences [INI]
- Mitsubishi International Corporation (through Organization: 三菱重工業株式会社 / Mitsubishi Heavy Industries (Japan) [MHI])
- Simons Foundation