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More on Wilson toroidal networks and torus blocks | | K.B. Alkalaev
; V.A. Belavin
; | | Date: |
20 Jul 2020 | | Abstract: | 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 $sl(2,mathbb{R})$ algebra. The resulting
expressions are given in two alternative forms using different ways to treat
multiple tensor products of $sl(2,mathbb{R})$ representations: (1) $3mj$
Wigner symbols and intertwiners of higher valence, (2) totally symmetric tensor
products of the fundamental $sl(2,mathbb{R})$ representation. | | Source: | arXiv, 2007.10494 | | Services: | Forum | Review | PDF | Favorites | |
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