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

by Slava Rychkov, Andreas Stergiou

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Submission summary

Authors (as Contributors): Slava Rychkov · Andreas Stergiou
Submission information
Arxiv Link: (pdf)
Date accepted: 2019-01-14
Date submitted: 2019-01-09 01:00
Submitted by: Stergiou, Andreas
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
Approach: Theoretical


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.

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.

Submission & Refereeing History

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Resubmission 1810.10541v4 on 9 January 2019

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