A no-go theorem for string warped compactifications

TL;DR

This paper establishes necessary conditions for certain string theory compactifications, showing that only specific geometries like Calabi-Yau manifolds support these configurations with preserved supersymmetry.

Contribution

It provides a no-go theorem demonstrating that only Calabi-Yau manifolds with constant dilaton can support heterotic and type II string warped compactifications preserving supersymmetry.

Findings

Heterotic string compactifications require Calabi-Yau manifolds with embedded spin connection.

Type II string compactifications are also limited to Calabi-Yau geometries under these conditions.

The results extend to compactifications in lower dimensions, such as six and two dimensions.

Abstract

We give necessary conditions for the existence of perturbative heterotic and common sector type II string warped compactifications preserving four and eight supersymmetries to four spacetime dimensions, respectively. In particular, we find that the only compactifications of heterotic string with the spin connection embedded in the gauge connection and type II strings are those on Calabi-Yau manifolds with constant dilaton. We obtain similar results for compactifications to six and to two dimensions.