Scale invariance, conformality, and generalized free fields

Journal Article · Tue Feb 16 00:00:00 EST 2016 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP02(2016)099· OSTI ID:1327254

Dymarsky, Anatoly ^[1]; Farnsworth, Kara ^[2]; Komargodski, Zohar ^[3]; Luty, Markus A. ^[2]; Prilepina, Valentina ^[2]

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1. Skolkovo Institute of Science and Technology, Moscow (Russia)
2. Univ. of California, Davis, CA (United States)
3. Weizmann Inst. of Science, Rehovot (Israel)

This paper addresses the question of whether there are 4D Lorentz invariant unitary quantum fi eld theories with scale invariance but not conformal invariance. We present an important loophole in the arguments of Luty-Polchinski-Rattazzi and Dymarsky-Komargodski-Schwimmer-Theisen that is the trace of the energy-momentum tensor T could be a generalized free field. In this paper we rule out this possibility. The key ingredient is the observation that a unitary theory with scale but not conformal invariance necessarily has a non-vanishing anomaly for global scale transformations. We show that this anomaly cannot be reproduced if T is a generalized free field unless the theory also contains a dimension-2 scalar operator. In the special case where such an operator is present it can be used to redefine ("improve") the energy-momentum tensor, and we show that there is at least one energy-momentum tensor that is not a generalized free field. In addition, we emphasize that, in general, large momentum limits of correlation functions cannot be understood from the leading terms of the coordinate space OPE. This invalidates a recent argument by Farnsworth-Luty-Prilepina (FLP). Finally, despite the invalidity of the general argument of FLP, some of the techniques turn out to be useful in the present context.

• Research Organization: Univ. of California, Davis, CA (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: FG02-91ER40674
• OSTI ID: 1327254
• Journal Information: Journal of High Energy Physics (Online), Vol. 2016, Issue 2; ISSN 1029-8479
• Publisher: Springer Berlin
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Space-Time Symmetries
Effective field theories