Hemisphere partition function and analytic continuation to the conifold point (Q1748970)

In this paper the authors study various types of linear \(U(1)\) gauged sigma models on two-dimensional disks with boundary. The hemisphere partition function is described in terms of differential equations of hypergeometric type, and the properties of analytic continuation inspected in detail. An interesting fact is that the computations done for the gauged linear sigma models (GLSM) actually correspond to compute the analytic continuation of a basis of periods on the mirror Calabi-Yau projective hypersurfaces, providing explicit applications to the cases of cubic, quartic and quintic Calabi-Yau hypersurfaces.