More on Wilson toroidal networks and torus blocks

Konstantin Alkalaev, Vladimir Belavin

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We consider the Wilson line networks of the Chern-Simons 3d gravity theory with toroidal boundary conditions which calculate global conformal blocks of degenerate quasi-primary operators in torus 2d CFT. After general discussion that summarizes and further extends results known in the literature we explicitly obtain the one-point torus block and two-point torus blocks through particular matrix elements of toroidal Wilson network operators in irreducible finite-dimensional representations of sl(2, ℝ) algebra. The resulting expressions are given in two alternative forms using different ways to treat multiple tensor products of sl(2, ℝ) representations: (1) 3mj Wigner symbols and intertwiners of higher valence, (2) totally symmetric tensor products of the fundamental sl(2, ℝ) representation.

Original languageEnglish
Article number121
JournalJournal of High Energy Physics
Issue number11
StatePublished - Nov 2020


  • AdS-CFT Correspondence
  • Chern-Simons Theories
  • Conformal and W Symmetry


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