Hemisphere Partition Function and Analytic Continuation to the Conifold Point

TL;DR

This paper develops a method to analytically continue the hemisphere partition function for certain GLSMs to the conifold point, enabling direct computation of D-brane central charges without mirror symmetry.

Contribution

It introduces a novel approach linking hemisphere partition functions to Mellin-Barnes integrals for analytic continuation in Calabi-Yau moduli space.

Findings

Successfully computed analytic continuation of D-brane central charges to the conifold point.

Applied methods explicitly to cubic, quartic, and quintic Calabi-Yau hypersurfaces.

Provided a mirror-independent technique for analyzing Calabi-Yau moduli.

Abstract

We show that the hemisphere partition function for certain U(1) gauged linear sigma models (GLSMs) with D-branes is related to a particular set of Mellin-Barnes integrals which can be used for analytic continuation to the singular point in the K\"ahler moduli space of an $h^{1,1}=1$ Calabi-Yau (CY) projective hypersurface. We directly compute the analytic continuation of the full quantum corrected central charge of a basis of geometric D-branes from the large volume to the singular point. In the mirror language this amounts to compute the analytic continuation of a basis of periods on the mirror CY to the conifold point. However, all calculations are done in the GLSM and we do not have to refer to the mirror CY. We apply our methods explicitly to the cubic, quartic and quintic CY hypersurfaces.