Conformal conserved currents in embedding space

Journal Article · 30 January 2022 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep01(2022)185 · OSTI ID:1976440

Fortin, Jean-François ^[1]; Ma, Wen-Jie ^[2]; Prilepina, Valentina ^[3]; Skiba, Witold ^[4]

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1. University of Laval, Quebec (Canada); Universite Laval, Quebec, QC (Canada)
2. University of Laval, Quebec (Canada)
3. University of Laval, Quebec (Canada); Lomonosov Moscow State University (Russian Federation)
4. Yale University, New Haven, CT (United States)

We study conformal conserved currents in arbitrary irreducible representations of the Lorentz group using the embedding space formalism. With the help of the operator product expansion, we first show that conservation conditions can be fully investigated by considering only two- and three-point correlation functions. We then find an explicitly conformally-covariant differential operator in embedding space that implements conservation based on the standard position space operator product expansion differential operator ∂μ, although the latter does not uplift to embedding space covariantly. The differential operator in embedding space that imposes conservation is the same differential operator $$D_{ijA}$$ used in the operator product expansion in embedding space. We provide several examples including conserved currents in irreducible representations that are not symmetric and traceless. With an eye on four-point conformal bootstrap equations for four conserved vector currents $$\langle JJJJ\rangle$$ and four energy-momentum tensors $$\langle TTTT\rangle$$, we mostly focus on conservation conditions for $$\langle JJ\mathcal{O}\rangle$$ and $$\langle TT\mathcal{O}\rangle$$. Finally, we reproduce and extend the consequences of conformal Ward identities at coincident points by determining three-point coefficients in terms of charges.

• Research Organization: Yale University, New Haven, CT (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP); Natural Sciences and Engineering Research Council of Canada (NSERC); China Scholarship Council
• Grant/Contract Number: SC0017660
• OSTI ID: 1976440
• Journal Information: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 1 Vol. 2022; ISSN 1029-8479
• Publisher: Springer NatureCopyright Statement
• Country of Publication: United States
• Language: English