Communications in Number Theory and Physics

Volume 11 (2017)

Number 1

Hemisphere partition function and analytic continuation to the conifold point

Pages: 73 – 164



Johanna Knapp (Institute for Theoretical Physics, Technische Universität, Wien, Austria)

Mauricio Romo (School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey, U.S.A.)

Emanuel Scheidegger (Mathematisches Institut, Albert-Ludwig-Universität, Freiburg, Germany)


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 Kähler 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.

Received 26 May 2016

Published 16 June 2017