Constraints on Perturbative RG Flows in Six Dimensions - INSPIRE

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Constraints on Perturbative RG Flows in Six Dimensions

Apr 6, 2016

17 pages

Published in:

JHEP 08 (2016) 010

Published: Aug 1, 2016

e-Print:

1604.01782 [hep-th]

DOI:

10.1007/JHEP08(2016)010

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Abstract: (Springer)

When conformal field theories (CFTs) are perturbed by marginally relevant deformations, renormalization group (RG) flows ensue that can be studied with perturbative methods, at least as long as they remain close to the original CFT. In this work we study such RG flows in the vicinity of six-dimensional unitary CFTs. Neglecting effects of scalar operators of dimension two and four, we use Weyl consistency conditions to prove the a-theorem in perturbation theory, and establish that scale implies conformal invariance. We identify a quantity that monotonically decreases in the flow to the infrared due to unitarity, showing that it does not agree with the one studied recently in the literature on the six-dimensional ϕ

^{3}

theory.

Note:

16 pages. v2: Mathematica notebook with consistency conditions included. v3: published version. Added derivation of equations 3.5, 3.13 to Mathematica notebook

Anomalies in Field and String Theories
Field Theories in Higher Dimensions
Renormalization Group
field theory: conformal
dimension: 6
renormalization group: flow
invariance: conformal
operator: dimension
operator: scalar
dimension: 2

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Figures(0)

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