We study three dimensional supersymmetric theories on with 2d boundary conditions at the boundaries , where or . We introduce supersymmetric indices of three dimensional theories on that couple to elliptic genera of 2d theories at the two boundaries. We evaluate the indices in terms of supersymmetric localization and study dualities on the . We consider the dimensional reduction of to and obtain the localization formula of 2d supersymmetric indices on . We illustrate computations of open string Witten indices based on gauged linear sigma models. Correlation functions of Wilson loops on agree with Euler pairings in the geometric phase and also agree with cylinder amplitudes for B-type boundary states of Gepner models in the Landau-Ginzburg phase.