Fractional two-branes, toric orbifolds and the quantum McKay correspondence

We systematically study and obtain the large-volume analogues of fractional two-branes on resolutions of the orbifolds ℂ3/ℤ n. We also study a generalisation of the McKay correspondence proposed in hep-th/0504164 called the quantum McKay correspondence by constructing duals to the fractional two-branes. Details are explicitly worked out for two examples - the crepant resolutions of ℂ3/ ℤ3 and ℂ3/ℤ5. © SISSA 2006.