Scale Invariance plus Unitarity Implies Conformal Invariance in Four Dimensions
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.
Cite
@article{arxiv.1309.4095,
title = {Scale Invariance plus Unitarity Implies Conformal Invariance in Four Dimensions},
author = {Kara Farnsworth and Markus A. Luty and Valentina Prelipina},
journal= {arXiv preprint arXiv:1309.4095},
year = {2014}
}
Comments
This paper has been withdrawn by the authors. Paper withdrawn. This paper claimed to give a proof that scale invariance implies conformal invariance using only the OPE and unitarity. This cannot be correct due to a counterexample. The mistake in the present paper is the use of the OPE in momentum space, which does not hold in the cases it was used in the argument. A detailed discussion of this point can be found in arXiv:1402.3208 and arXiv:1402.6322