Abstract
To explore the possibility of self-organized criticality, we look for CFTs without any relevant scalar deformations (a.k.a. dead-end CFTs) within power-counting renormalizable quantum field theories with a weakly coupled Lagrangian description. In three dimensions, the only candidates are pure (Abelian) gauge theories, which may be further deformed by Chern-Simons terms. In four dimensions, we show that there are infinitely many non-trivial candidates based on chiral gauge theories. Using the three-loop beta functions, we compute the gap of scaling dimensions above the marginal value, and it can be as small as \( \mathcal{O}\left(1{0}^{-5}\right) \) and robust against the perturbative corrections. These classes of candidates are very weakly coupled and our perturbative conclusion seems difficult to refute. Thus, the hypothesis that non-trivial dead-end CFTs do not exist is likely to be false in four dimensions.
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Nakayama, Y. Perturbative search for dead-end CFTs. J. High Energ. Phys. 2015, 46 (2015). https://doi.org/10.1007/JHEP05(2015)046
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DOI: https://doi.org/10.1007/JHEP05(2015)046
Keywords
- Conformal and W Symmetry
- Renormalization Group