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arXiv · 1309.4095

Scale Invariance plus Unitarity Implies Conformal Invariance in Four Dimensions

Kara Farnsworth·Markus A. Luty·Valentina Prelipina
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Abstract

We give a non-perturbative proof that any 4D unitary and Lorentz-invariant quantum field theory with a conserved scale current is in fact conformally invariant. We show that any scale invariant theory (unitary or not) must have either a vanishing anomaly for global scale transformations or an operator of spin 2 and dimension 2. Neither of these possibilities is allowed for unitary theories, proving the result. This is also a strong constraint on non-unitary Euclidean theories with scale but not conformal invariance, suggesting the conjecture that all such theories are free field theories.

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Kara Farnsworth, Markus A. Luty, Valentina Prelipina. 2013-09-16. Scale Invariance plus Unitarity Implies Conformal Invariance in Four Dimensions. https://arxiv.org/abs/1309.4095

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