  We propose a general formula for perturbative-in-alpha' corrections to the
Kahler potential on the quantum Kahler moduli space of Calabi-Yau n-folds, for
any n, in their asymptotic large volume regime. The knowledge of such
perturbative corrections provides an important ingredient needed to analyze the
full structure of this Kahler potential, including nonperturbative corrections
such as the Gromov-Witten invariants of the Calabi-Yau n-folds. We argue that
the perturbative corrections take a universal form, and we find that this form
is encapsulated in a specific additive characteristic class of the Calabi-Yau
n-fold which we call the log Gamma class, and which arises naturally in a
generalization of Mukai's modified Chern character map. Our proposal is
inspired heavily by the recent observation of an equality between the partition
function of certain supersymmetric, two-dimensional gauge theories on a
two-sphere, and the aforementioned Kahler potential. We further strengthen our
proposal by comparing our findings on the quantum Kahler moduli space to the
complex structure moduli space of the corresponding mirror Calabi-Yau geometry.
