  Many N=(2,2) two-dimensional nonlinear sigma models with Calabi-Yau target
spaces admit ultraviolet descriptions as N=(2,2) gauge theories (gauged linear
sigma models). We conjecture that the two-sphere partition function of such
ultraviolet gauge theories -- recently computed via localization by Benini et
al. and Doroud et al. -- yields the exact K\"ahler potential on the quantum
K\"ahler moduli space for Calabi-Yau threefold target spaces. In particular,
this allows one to compute the genus zero Gromov-Witten invariants for any such
Calabi-Yau threefold without the use of mirror symmetry. More generally, when
the infrared superconformal fixed point is used to compactify string theory,
this provides a direct method to compute the spacetime K\"ahler potential of
certain moduli (e.g., vector multiplet moduli in type IIA), exactly in
{\alpha}'. We compute these quantities for the quintic and for R{\o}dland's
Pfaffian Calabi-Yau threefold and find agreement with existing results in the
literature. We then apply our methods to a codimension four determinantal
Calabi-Yau threefold in P^7, recently given a nonabelian gauge theory
description by the present authors, for which no mirror Calabi-Yau is currently
known. We derive predictions for its Gromov-Witten invariants and verify that
our predictions satisfy nontrivial geometric checks.
