Global conformal blocks via shadow formalism

Vladimir Belavin, J. Ramos Cabezas

Research output: Contribution to journalArticlepeer-review


We study sl2 and sl3 global conformal blocks on a sphere and a torus, using the shadow formalism. These blocks arise in the context of Virasoro and W3 conformal field theories in the large central charge limit. In the sl2 case, we demonstrate that the shadow formalism yields the known expressions in terms of conformal partial waves. Then, we extend this approach to the sl3 case and show that it allows to build simple integral representations for sl3 global blocks. We demonstrate this construction on two examples: the four-point block on the sphere and the one-point torus block.

Original languageEnglish
Article number167
JournalJournal of High Energy Physics
Issue number2
StatePublished - Feb 2024


  • AdS-CFT Correspondence
  • Conformal and W Symmetry
  • Field Theories in Lower Dimensions


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