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We analyze conformal blocks with multiple (semi-)degenerate field insertionsin Liouville/Toda conformal field theories an show that their vector space isfully reproduced by the four-dimensional limit of open topological stringamplitudes on the strip with generic boundary conditions associated to asuitable quiver gauge theory. As a byproduct we identify the non-abelian vortexpartition function with a specific fusion channel of degenerate conformalblocks.

The Liouville side of the Vortex