N=2 gauge theories on unoriented/open four-manifolds and their AGT counterparts

We compute the exact path integral of N = 2 supersymmetric gauge theories with general gauge group on RP4 and a Z(2)-quotient of the hemi-S-4. By specializing to SU(2) superconformal quivers, we show that these, together with hemi-S-4 partition functions, compute Liouville correlators on unoriented/open Riemann surfaces. We perform explicit checks for Riemann surfaces obtained as Z(2) quotients of the sphere and the torus. We also discuss the coupled 3d-4d systems associated to Liouville amplitudes with boundary punctures.