Bonelli, GiulioTanzini, AlessandroZhao, Jian2013-04-042013-04-042011-07-11https://openscience.sissa.it/handle/1963/657425pages,11figures ; SISSA preprint - 36/2011/FM-EPWe analyze conformal blocks with multiple (semi-)degenerate field insertions in Liouville/Toda conformal field theories an show that their vector space is fully reproduced by the four-dimensional limit of open topological string amplitudes on the strip with generic boundary conditions associated to a suitable quiver gauge theory. As a byproduct we identify the non-abelian vortex partition function with a specific fusion channel of degenerate conformal blocks.enSISSAPreprint