Abstract
There has been recent interest in the question of whether four dimensional scale invariant unitary quantum field theories are actually conformally invariant. In this note we present a complete analysis of possible scale anomalies in correlation functions of the trace of the stress-energy tensor in such theories. We find that 2-, 3- and 4-point functions have a non-trivial anomaly while connected higher point functions are non-anomalous. We pay special attention to semi-local contributions to correlators (terms with support on a set containing both coincident and separated points) and show that the anomalies in 3- and 4-point functions can be accounted for by such contributions. We discuss the implications of the our results for the question of scale versus conformal invariance.
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Bzowski, A., Skenderis, K. Comments on scale and conformal invariance. J. High Energ. Phys. 2014, 27 (2014). https://doi.org/10.1007/JHEP08(2014)027
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DOI: https://doi.org/10.1007/JHEP08(2014)027