Higher-Order Corrections to Non-Compact Calabi-Yau Manifolds in String Theory

TL;DR

This paper investigates higher-order -corrections to non-compact Calabi-Yau manifolds in string theory, analyzing their effects on geometry and supersymmetry, and deriving modified solutions for specific metrics.

Contribution

It provides the first detailed analysis of ^3-order corrections on non-compact Calabi-Yau spaces, including derivation of modified Killing-spinor equations and solutions.

Findings

Calabi-Yau spaces remain Ke4hler but are no longer Ricci-flat after corrections.

Derived first-order equations for modified supersymmetric solutions.

Analyzed boundary terms for Euler characteristic in six and eight dimensions.

Abstract

At the leading order, the low-energy effective field equations in string theory admit solutions of the form of products of Minkowski spacetime and a Ricci-flat Calabi-Yau space. The equations of motion receive corrections at higher orders in \alpha', which imply that the Ricci-flat Calabi-Yau space is modified. In an appropriate choice of scheme, the Calabi-Yau space remains Kahler, but is no longer Ricci-flat. We discuss the nature of these corrections at order {\alpha'}^3, and consider the deformations of all the known cohomogeneity one non-compact Kahler metrics in six and eight dimensions. We do this by deriving the first-order equations associated with the modified Killing-spinor conditions, and we thereby obtain the modified supersymmetric solutions. We also give a detailed discussion of the boundary terms for the Euler complex in six and eight dimensions, and apply the results to all the cohomogeneity one examples.