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arXiv · 0910.1087

Scale Invariance + Unitarity => Conformal Invariance?

Daniele Dorigoni·Slava Rychkov
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Abstract

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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Daniele Dorigoni, Slava Rychkov. 2009-10-06. Scale Invariance + Unitarity => Conformal Invariance?. https://arxiv.org/abs/0910.1087

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