Seven-Point Conformal Blocks in the Extended Snowflake Channel and Beyond

Understand

Seven-point functions have two inequivalent topologies or channels.

• The comb channel has been computed previously and here we compute scalar conformal blocks in the extended snowflake channel in $d$ dimensions.
• Our computation relies on the known action of the differential operator that sets up the operator product expansion in embedding space.
• The scalar conformal blocks in the extended snowflake channel are obtained as a power series expansion in the conformal cross-ratios whose coefficients are a triple sum of the hypergeometric type.