The gauged linear sigma model is a supersymmetric gauge theory in two dimensions which captures information about Calabi-Yaus and their moduli spaces. Recent results of supersymmetric localization provide new tools for computing quantum corrections in string compactifications. This talk will focus in particular on the hemisphere partition function in the GLSM which computes the quantum corrected central charge of B-type D-branes. Several concrete examples of GLSMs and the application of the hemisphere partition function in the context of transporting D-branes in the Kahler moduli space will be given.
