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- W4306291738 abstract "A bstract We consider the conformal block decomposition in arbitrary exchange channels of a two-dimensional conformal field theory on a torus. The channels are described by diagrams built of a closed loop with external legs (a necklace sub-diagram) and trivalent vertices forming trivalent trees attached to the necklace. Then, the n -point torus conformal block in any channel can be obtained by acting with a number of OPE operators on the k -point torus block in the necklace channel at k = 1 , … , n . Focusing on the necklace channel, we go to the large- c regime, where the Virasoro algebra truncates to the sl (2 , ℝ) subalgebra, and obtain the system of the Casimir equations for the respective k -point global conformal block. In the plane limit, when the torus modular parameter q → 0, we explicitly find the Casimir equations on a plane which define the ( k + 2)-point global conformal block in the comb channel. Finally, we formulate the general scheme to find Casimir equations for global torus blocks in arbitrary channels." @default.
- W4306291738 created "2022-10-15" @default.
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- W4306291738 date "2022-10-14" @default.
- W4306291738 modified "2023-09-30" @default.
- W4306291738 title "Torus conformal blocks and Casimir equations in the necklace channel" @default.
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- W4306291738 doi "https://doi.org/10.1007/jhep10(2022)091" @default.
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