Deconstructing Conformal Blocks in 4D CFT

Abstract

We show how conformal partial waves (or conformal blocks) of spinor/tensor correlators can be related to each other by means of differential operators in four dimensional conformal field theories. We explicitly construct such differential operators for all possible conformal partial waves associated to four-point functions of arbitrary traceless symmetric operators. Our method allows any conformal partial wave to be extracted from a few "seed" correlators, simplifying dramatically the computation needed to bootstrap tensor correlators.

33 pages; v2: minor improvements and typos fixed, matches JHEP published version; v3: $X^{+}$ factors fixed in eqs.(2.3) and (2.4), minor improvements

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Cited by in corpus (4)

• Quantum Integrable Systems from Conformal Blocks
• Efficient Rules for All Conformal Blocks
• Conformal Two-Point Correlation Functions from the Operator Product Expansion
• Superconformal Partial Waves for Stress-tensor Multiplet Correlator in $4D$ $\mathcal{N}=2$ SCFTs