Scale-invariant breaking of conformal symmetry
Anatoly Dymarsky, Alexander Zhiboedov
TL;DR
This paper demonstrates that unitary scale-invariant but not conformal-invariant field theories embedded in CFTs are necessarily free theories, explaining the triviality of known examples in four dimensions across all spacetime dimensions.
Contribution
It proves that any such SFT embedded in a unitary CFT must be a free theory, providing a general explanation for their triviality in four dimensions.
Findings
Embedded SFTs are free theories
Triviality of known SFTs in four dimensions
Applicability across arbitrary spacetime dimensions
Abstract
Known examples of unitary relativistic scale but not conformal-invariant field theories (SFTs) can be embedded into conventional conformal field theories (CFTs). We show that any SFT which is a subsector of a unitary CFT is a free theory. Our discussion applies to an arbitrary number of spacetime dimensions and explains triviality of known SFTs in four spacetime dimensions. We comment on examples of unitary SFTs which are not captured by our construction.
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