  To compute the string one-loop correction to the Kahler potential of moduli
fields of string compactifications in Einstein-frame, one must compute: the
string one-loop correction to the Einstein-Hilbert action, the string one-loop
correction to the moduli kinetic terms, the string one-loop correction to the
definition of the holomorphic coordinates. In this note, we compute the string
one-loop correction to the Einstein-Hilbert action of type II string theory
compactified on orientifolds of Calabi-Yau threefolds. We find that the
one-loop correction is determined by the new supersymmetric index studied by
Cecotti, Fendley, Intriligator, and Vafa. As a simple application, we apply our
results to estimate the size of the one-loop corrections around a conifold
point in the Kahler moduli space.
