Built on

Cambridge University Press, 1984
J. C. Collins, Renormalization: An Introduction to Renormalization, the Renormalization Group and the Operator-Product Expansion · 1984
Earlier work this paper cites.
A. Zamolodchikov, “Irreversibility of the flux of the renormalization group in a 2D field theory,” JETP Lett
1986
Earlier work this paper cites.
J. Polchinski, “Scale and conformal invariance in quantum field theory,” Nucl.Phys
1988
Earlier work this paper cites.
I. Jack and H. Osborn, “Analogs for the c c Theorem for Four-dimensional Renormalizable Field Theories,” Nucl.Phys
1990
Earlier work this paper cites.
H. Osborn, “Weyl consistency conditions and a local renormalization group equation for general renormalizable field theories,” Nucl.Phys
1991
Earlier work this paper cites.
L. Girardello, M. Petrini, M. Porrati, and A. Zaffaroni, “Novel local CFT and exact results on perturbations of N=4 superYang Mills from AdS dynamics,” JHEP
1998
Earlier work this paper cites.
D. Freedman, S. Gubser, K. Pilch, and N. Warner, “Renormalization group flows from holography supersymmetry and a c theorem,” Adv.Theor.Math.Phys
1999
Earlier work this paper cites.

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S. El-Showk, Y. Nakayama, and S. Rychkov, “What Maxwell Theory in D ≠ 4 D\neq 4 teaches us about scale and conformal invariance,” Nucl.Phys
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Then

H. Casini, M. Huerta, and R. C. Myers, “Towards a derivation of holographic entanglement entropy,” JHEP
Original
2011
Later among the works it cites.
Z. Komargodski, “The Constraints of Conformal Symmetry on RG Flows,” JHEP
Original
2012
Later among the works it cites.
H. Elvang, D. Z. Freedman, L.-Y. Hung, M. Kiermaier, R. C. Myers, et al
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2012
Later among the works it cites.
H. Casini and M. Huerta, “On the RG running of the entanglement entropy of a circle,” Phys.Rev
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2012
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M. A. Luty, J. Polchinski, and R. Rattazzi, “The a a -theorem and the asymptotics of 4D quantum field theory,” JHEP
Original

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2014

Scale Invariance, Conformality, and Generalized Free Fields

Dymarsky, Anatoly, Farnsworth, Kara, Komargodski, Zohar et al.

Understand

This paper addresses the question of whether there are 4D Lorentz invariant unitary quantum field theories with scale invariance but not conformal invariance.

An important loophole in the arguments of Luty-Polchinski-Rattazzi and Dymarsky-Komargodski-Schwimmer-Theisen is that 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.

Built on

Cambridge University Press, 1984
J. C. Collins, Renormalization: An Introduction to Renormalization, the Renormalization Group and the Operator-Product Expansion · 1984
Earlier work this paper cites.
A. Zamolodchikov, “Irreversibility of the flux of the renormalization group in a 2D field theory,” JETP Lett
1986
Earlier work this paper cites.
J. Polchinski, “Scale and conformal invariance in quantum field theory,” Nucl.Phys
1988
Earlier work this paper cites.
I. Jack and H. Osborn, “Analogs for the c c Theorem for Four-dimensional Renormalizable Field Theories,” Nucl.Phys
1990
Earlier work this paper cites.
H. Osborn, “Weyl consistency conditions and a local renormalization group equation for general renormalizable field theories,” Nucl.Phys
1991
Earlier work this paper cites.
L. Girardello, M. Petrini, M. Porrati, and A. Zaffaroni, “Novel local CFT and exact results on perturbations of N=4 superYang Mills from AdS dynamics,” JHEP
1998
Earlier work this paper cites.
D. Freedman, S. Gubser, K. Pilch, and N. Warner, “Renormalization group flows from holography supersymmetry and a c theorem,” Adv.Theor.Math.Phys
1999
Earlier work this paper cites.