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Scale Invariance + Unitarity => Conformal Invariance?

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arxiv 0910.1087 v1 pith:IJSDX4XO submitted 2009-10-06 hep-th cond-mat.stat-mechhep-ph

Daniele Dorigoni , Slava Rychkov This is my paper · ORCID
classification hep-thcond-mat.stat-mechhep-ph
keywords counterexamplesinvariancedimensionsproofscaletheoriesconformalconformality
verification ladder T0 review T1 audit T2 compute T3 formal
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We revisit the long-standing conjecture that in unitary field theories, scale invariance implies conformality. We explain why the Zamolodchikov-Polchinski proof in D=2 does not work in higher dimensions. We speculate which new ideas might be helpful in a future proof. We also search for possible counterexamples. We consider a general multi-field scalar-fermion theory with quartic and Yukawa interactions. We show that there are no counterexamples among fixed points of such models in 4-epsilon dimensions. We also discuss fake counterexamples, which exist among theories without a stress tensor.

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  1. Parisi-Sourlas Supertranslation and Scale without Conformal symmetry

    hep-th 2024-11 accept novelty 7.0 of 10

    Supertranslation symmetry protects the virial current's scaling dimension, giving eight perturbative scale-invariant but non-conformal fixed points in a quartic superfield model.

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