English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this note, we present an alternative representation of the conformal blockwith external scalars in general spacetime dimensions in terms of a finitesummation over Appell fourth hypergeometric function ${\bf{F}}_4$. We alsoconstruct its generalization to the non-local primary exchange operator withcontinuous spin and its corresponding Mellin representation which are relevantfor Lorentzian spacetime. Using these results we apply the Lorentzian inversionformula to compute so-called crossing kernel in general spacetime dimensions,the resultant expression can be written as a double infinite summation overcertain Kamp\~{e} de F\~{e}riet hypergeometric functions with the correctdouble trace operator singularity structures. We also include somecomplementary computations in AdS space, demonstrating the orthogonality ofconformal blocks and performing the decompositions.

On Conformal Block, Crossing Kernel and Multi-variable Hypergeometric Functions