Scale invariance, conformality, and generalized free fields
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 LutyPolchinskiRattazzi and DymarskyKomargodskiSchwimmerTheisen that is the trace of the energymomentum 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 nonvanishing 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 dimension2 scalar operator. In the special case where such an operator is present it can be used to redefine ("improve") the energymomentum tensor, and we show that there is at least one energymomentum 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 FarnsworthLutyPrilepina (FLP). Finally, despite the invalidity of the general argument of FLP, some of the techniques turn out to be useful in themore »
 Authors:

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 Skolkovo Institute of Science and Technology, Moscow (Russia)
 Univ. of California, Davis, CA (United States)
 Weizmann Inst. of Science, Rehovot (Israel)
 Publication Date:
 Grant/Contract Number:
 FG0291ER40674
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 2; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Research Org:
 Univ. of California, Davis, CA (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; SpaceTime Symmetries; Effective field theories
 OSTI Identifier:
 1327254
Dymarsky, Anatoly, Farnsworth, Kara, Komargodski, Zohar, Luty, Markus A., and Prilepina, Valentina. Scale invariance, conformality, and generalized free fields. United States: N. p.,
Web. doi:10.1007/JHEP02(2016)099.
Dymarsky, Anatoly, Farnsworth, Kara, Komargodski, Zohar, Luty, Markus A., & Prilepina, Valentina. Scale invariance, conformality, and generalized free fields. United States. doi:10.1007/JHEP02(2016)099.
Dymarsky, Anatoly, Farnsworth, Kara, Komargodski, Zohar, Luty, Markus A., and Prilepina, Valentina. 2016.
"Scale invariance, conformality, and generalized free fields". United States.
doi:10.1007/JHEP02(2016)099. https://www.osti.gov/servlets/purl/1327254.
@article{osti_1327254,
title = {Scale invariance, conformality, and generalized free fields},
author = {Dymarsky, Anatoly and Farnsworth, Kara and Komargodski, Zohar and Luty, Markus A. and Prilepina, Valentina},
abstractNote = {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 LutyPolchinskiRattazzi and DymarskyKomargodskiSchwimmerTheisen that is the trace of the energymomentum 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 nonvanishing 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 dimension2 scalar operator. In the special case where such an operator is present it can be used to redefine ("improve") the energymomentum tensor, and we show that there is at least one energymomentum 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 FarnsworthLutyPrilepina (FLP). Finally, despite the invalidity of the general argument of FLP, some of the techniques turn out to be useful in the present context.},
doi = {10.1007/JHEP02(2016)099},
journal = {Journal of High Energy Physics (Online)},
number = 2,
volume = 2016,
place = {United States},
year = {2016},
month = {2}
}