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Title:
Conformal Conserved Currents in Embedding Space. A General Framework
Speaker:
Abstract:
In this talk, I will consider conformal conserved currents in arbitrary irreducibleLorentz representations in the context of the embedding space OPE formalismdue to Fortin and Skiba (DOI:10.1007/JHEP06(2020)028). I will begin by givingsome background on the formalism. I will then briefly discuss how conservationconditions on higher-point functions can be fully enforced within this frameworkby restricting attention to two- and three-point correlation functions. Next, I willdescribe how to construct an explicitly conformally-covariant conserved currentdifferential operator in this context. As I will argue, the appropriate operatoris none other than the OPE differential operator in embedding space, revealingan interesting correspondence between the OPE differential operators and theconserved current differential operators in embedding space and the equivalentobjects in position space. I will subsequently explore several explicit examples ofconserved currents in various irreducible representations, primarily focusing onconservation conditions for hJJOi. Further, I will summarize the principal resultsof the analysis relevant for the conformal bootstrap of hT T T Ti and hJJJJi.Lastly, I will examine how to reproduce and extend the consequences of conformalWard identities at coincident points within this framework.
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