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Scale-invariant breaking of conformal symmetry · Around

2015

Scale-invariant breaking of conformal symmetry

Dymarsky, Anatoly, Zhiboedov, Alexander

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Known examples of unitary relativistic scale but not conformal-invariant field theories (SFTs) can be embedded into conventional conformal field theories (CFTs).

We show that any SFT which is a subsector of a unitary CFT is a free theory.
Our discussion applies to an arbitrary number of spacetime dimensions and explains triviality of known SFTs in four spacetime dimensions.
We comment on examples of unitary SFTs which are not captured by our construction.

Built on

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J. Polchinski, “Scale and Conformal Invariance in Quantum Field Theory,” Nucl. Phys. B 303
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J. L. Cardy, “Is There a c Theorem in Four-Dimensions?,” Phys. Lett. B 215
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I. R. Klebanov and A. M. Polyakov, “AdS dual of the critical O(N) vector model,” Phys. Lett. B 550
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Earlier work this paper cites.

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A. Dymarsky, Z. Komargodski, A. Schwimmer and S. Theisen, “On Scale and Conformal Invariance in Four Dimensions,” arXiv:1309.2921 [hep-th]
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A. Dymarsky, K. Farnsworth, Z. Komargodski, M. A. Luty and V. Prilepina, “Scale Invariance, Conformality, and Generalized Free Fields,” arXiv:1402.6322 [hep-th]
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K. Yonekura, “Unitarity, Locality, and Scale versus Conformal Invariance in Four Dimensions,” arXiv:1403.4939 [hep-th]
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D. Dorigoni and V. S. Rychkov, “Scale Invariance + Unitarity =¿ Conformal Invariance?,” arXiv:0910.1087 [hep-th]
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M. A. Vasiliev, “Higher spin gauge theories: Star product and AdS space,” In Shifman, M.A. (ed.): The many faces of the superworld 533-610 [hep-th/9910096]
Cited in the paper.

Then

J. Maldacena and A. Zhiboedov, “Constraining Conformal Field Theories with A Higher Spin Symmetry,” J. Phys. A 46
Original
2013
Later among the works it cites.
M. A. Luty, J. Polchinski and R. Rattazzi, “The a a -theorem and the Asymptotics of 4D Quantum Field Theory,” JHEP 1301
Original
2013
Later among the works it cites.
Y. Nakayama, “Scale invariance vs conformal invariance,” Phys. Rept. 569
Original
2015
Closest in time.

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