Instantons and conformal blocks

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A systematic method to construct 4d N=2 supersymmetric theories by compactifying M5-branes on a Riemann surface was found by Gaiotto last year.
This suggests that any physical quantity of the 4d theory should be reflected in another physical quantity of the 2d theory living on the Riemann surface.
Indeed, one finds that the instanton partition function of the 4d theories equals the conformal blocks of the 2d theory.
I would like to illustrate this construction through explicit examples.