Ricci-flat supertwistor spaces

TL;DR

This paper demonstrates that supertwistor spaces derived from hyperkahler cones with balanced bosonic and fermionic coordinates are Ricci-flat, establishing their Calabi-Yau property, and explores their deformations.

Contribution

It introduces a method to construct Ricci-flat supertwistor spaces via Kahler quotients of hyperkahler cones and analyzes their deformation space.

Findings

Supertwistor spaces are Ricci-flat and Calabi-Yau.

Deformations of the underlying hyperkahler cones induce deformations of supertwistor spaces.

Certain infinitesimal deformations preserve Ricci-flatness.

Abstract

We show that supertwistor spaces constructed as a Kahler quotient of a hyperkahler cone (HKC) with equal numbers of bosonic and fermionic coordinates are Ricci-flat, and hence, Calabi-Yau. We study deformations of the supertwistor space induced from deformations of the HKC. We also discuss general infinitesimal deformations that preserve Ricci-flatness.