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What Maxwell theory in d ≠ 4 teaches us about scale and conformal invariance

El-Showk, Sheer and Nakayama, Yu and Rychkov, Slava (2011) What Maxwell theory in d ≠ 4 teaches us about scale and conformal invariance. Nuclear Physics B, 848 (3). pp. 578-593. ISSN 0550-3213. doi:10.1016/j.nuclphysb.2011.03.008.

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The free Maxwell theory in d ≠ 4 dimensions provides a physical example of a unitary, scale invariant theory which is NOT conformally invariant. The easiest way to see this is that the field strength operator F_(μν) is neither a primary nor a descendant. We show how conformal multiplets can be completed, and conformality restored, by adding new local operators to the theory. In d ≥ 5, this can only be done by sacrificing unitarity of the extended Hilbert space. We analyze the full symmetry structure of the extended theory, which turns out to be related to the OSp(d,2|2) superalgebra.

Item Type:Article
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URLURL TypeDescription
Rychkov, Slava0000-0002-5847-1011
Additional Information:© 2011 Elsevier B.V. Received 14 February 2011; accepted 11 March 2011. Available online 16 March 2011. S.R. is grateful to Jan Troost, Manuela Kulaxizi and Andrei Parnachev for useful discussions. Y.N. thanks John Cardy for the encouraging and stimulating correspondence on the subject. S.E. would like to thank the CEA Saclay for hospitality during the completion of part of this work. The research of S.E. is partially supported by the Netherlands Organisation for Scientific Research (NWO) under a Rubicon grant. The work of S.R. was supported in part by the European Programme “Unification in the LHC Era”, contract PITN-GA-2009-237920 (UNILHC). The work of Y.N. is supported by Sherman Fairchild Fellowship at California Institute of Technology.
Group:Caltech Theory
Funding AgencyGrant Number
Netherlands Organisation for Scientific Research (NWO) Rubicon GrantUNSPECIFIED
European Programme Unification in the LHC Era (UNILHC)PITN-GA-2009-237920
Caltech Sherman Fairchild FellowshipUNSPECIFIED
Issue or Number:3
Record Number:CaltechAUTHORS:20110531-091938425
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Official Citation:Sheer El-Showk, Yu Nakayama, Slava Rychkov, What Maxwell theory in d[not equal to]4 teaches us about scale and conformal invariance, Nuclear Physics B, Volume 848, Issue 3, 21 July 2011, Pages 578-593, ISSN 0550-3213, DOI: 10.1016/j.nuclphysb.2011.03.008. (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:23829
Deposited By: Ruth Sustaita
Deposited On:31 May 2011 16:51
Last Modified:09 Nov 2021 16:18

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