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

## TL;DR

This paper calculates the one-loop string correction to the Einstein-Hilbert action in type II compactifications, revealing its dependence on a supersymmetric index and estimating effects near conifold points.

## Contribution

It provides the first explicit computation of the one-loop correction to the Einstein-Hilbert term in type II string theory on Calabi-Yau orientifolds, linking it to a supersymmetric index.

## Key findings

- One-loop correction is governed by a supersymmetric index.
- The correction's size can be estimated near conifold points.
- Results have implications for moduli space dynamics.

## Abstract

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.