Weight shifting operators and conformal blocks
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Publication:1748772
DOI10.1007/JHEP02(2018)081zbMATH Open1387.81323arXiv1706.07813WikidataQ106730135 ScholiaQ106730135MaRDI QIDQ1748772
Author name not available (Why is that?)
Publication date: 14 May 2018
Published in: (Search for Journal in Brave)
Abstract: We introduce a large class of conformally-covariant differential operators and a crossing equation that they obey. Together, these tools dramatically simplify calculations involving operators with spin in conformal field theories. As an application, we derive a formula for a general conformal block (with arbitrary internal and external representations) in terms of derivatives of blocks for external scalars. In particular, our formula gives new expressions for "seed conformal blocks" in 3d and 4d CFTs. We also find simple derivations of identities between external-scalar blocks with different dimensions and internal spins. We comment on additional applications, including derivation of recursion relations for general conformal blocks, reducing inversion formulae for spinning operators to inversion formulae for scalars, and deriving identities between general 6j symbols (Racah-Wigner coefficients/"crossing kernels") of the conformal group.
Full work available at URL: https://arxiv.org/abs/1706.07813
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