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General Properties of Multiscalar RG Flows in $d=4-\varepsilon$
by Slava Rychkov, Andreas Stergiou
Submission summary
| Authors (as registered SciPost users): | Slava Rychkov · Andreas Stergiou |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/1810.10541v4 (pdf) |
| Date accepted: | Jan. 14, 2019 |
| Date submitted: | Jan. 9, 2019, 1 a.m. |
| Submitted by: | Andreas Stergiou |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
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.
Author comments upon resubmission
Published as SciPost Phys. 6, 008 (2019)