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Perturbative search for dead-end CFTs · Around

2015

Perturbative search for dead-end CFTs

Nakayama, Yu

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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 $\mathcal{O}(10^{-5})$ and robust against the perturbative corrections.

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