On string one-loop correction to the Einstein-Hilbert term and its implications on the Kahler potential

Understand

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.