On one-loop corrected dilaton action in string theory

This manuscript concerns string one-loop corrections to the Kahler potential in 4d N=1 vacua of string theories, and it largely consists of two parts. In the first part, we compute the string one-loop correction to the dilaton kinetic term in heterotic string theories, and we show that the dilaton kinetic term is not renormalized at one-loop. After reviewing the well-known result on the string one-loop correction to the Kahler potential in heterotic string theories, we explain how this result can be reconciled with the known result in the literature. In the second part, we study the dilaton dependence of the one-loop corrected Kahler potential in type II string theories. To do so, we compute the string one-loop correction to the kinetic action of the 4d-dilaton in type II string theories compactified on orientifolds of Calabi-Yau threefolds. We find that the string one-loop corrected 4d dilaton kinetic term is determined by the Witten index and the new supersymmetric index of the string worldsheet CFT.