The All-Genus String Effective Action

TL;DR

This paper derives a comprehensive all-genus string effective action in low-energy massless backgrounds, revealing how dilaton vacuum expectation values are determined and confirming non-renormalization properties in certain compactified models.

Contribution

It provides a formula for the all-genus string effective action with implications for dilaton determination and non-renormalization in compactified models.

Findings

Dilaton vacuum expectation value can be determined from the all-genus effective action.

In Kähler compactifications, the target-space dilaton is constrained by background fields.

Tree-level Kähler potential and superpotential remain unchanged by higher-genus effects.

Abstract

We use the off-shell string effective action method developed by E.S. Fradkin and A.A. Tseytlin to obtain the formula for all-genus string effective action with and without compactification at the low-energy approximation in the massless background fields. We find that for the bosonic string, one can determine the dilaton vacuum expectation value from the all-genus effective action because of the nontrivial dependence of potential energy on dilaton. For compactified four-dimensional string models, if one requires that the target-space dilaton field lie on a K\"ahler manifold, we obtain a constraint which will specify the worldsheet dilaton in terms of the constant background fields. We also show that under this constraint, the tree-level k\"ahlar potential and superpotential are not changed by the higher-genus effect. This proves again the non-renormalization theorem for a string moving in massless background fields in the low-energy approximation.