Stringy Corrections to Heterotic SU(3)-Geometry

TL;DR

This paper investigates the effects of stringy $oldsymbol{rac{oldsymbol{ ext{alpha}}'}{2}}$ corrections on heterotic compactifications with SU(3) structure, revealing how these corrections alter geometric and gauge properties.

Contribution

It provides a detailed analysis of $oldsymbol{rac{oldsymbol{ ext{alpha}}'}{2}}$ corrections to the supersymmetry algebra and geometric structures in heterotic SU(3) compactifications, including new integrability conditions.

Findings

Curvature of tangent bundle connection gains a nonzero (0,2) component.

An integrability condition for solutions related to the graviton equation of motion.

$oldsymbol{rac{oldsymbol{ ext{alpha}}'}{2}}$ corrections can disrupt semi-classical instanton intuition.

Abstract

We analyse the $\alpha'^2$ corrections to the supersymmetry algebra constructed by Bergshoeff--de Roo for heterotic compactifications on SU(3) manifolds. The geometry is complex and conformally balanced. We find an integrability condition for solutions related to the graviton equation of motion together with a correction that is pure gauge. We derive the same condition independently from hermitian geometry. The curvature of the tangent bundle connection acquires a nonzero (0,2) component and thus is not an instanton, illustrating how $\alpha'$-corrections can disrupt semi-classical intuition.