Crosscap states in N=2 Liouville theory

We construct crosscap states in the N=2 Liouville theory from the modular bootstrap method. We verify our results by comparing it with the calculation from the minisuperspace approximation and by checking the consistency with the conformal bootstrap equation. Various overlaps with other known branes are studied. We further discuss the topological nature of the discrete terms in the crosscap wavefunction and their connection with the Landau-Ginzburg approach in a nontrivial dilaton background. We find that it can be mapped to the Landau-Ginzburg theory with a negative power superpotential by a simple change of variables, extending the known duality to the open string sector. Possible applications to the two-dimensional noncritical string theories and supersymmetric orientifolds in the higher dimension are also discussed.