N=2 Supersymmetric Calabi-Yau Hypersurface Sigma-Models on Curved Two-Dimensions

TL;DR

This paper explores how curved two-dimensional space affects N=2 supersymmetric sigma models related to Calabi-Yau hypersurfaces, maintaining their core features and connecting to superstring theory.

Contribution

It demonstrates the preservation of key properties of Calabi-Yau sigma models on curved worldsheets with partial local supersymmetry, extending their applicability.

Findings

Sigma models maintain their relation between Calabi-Yau and Landau-Ginzburg models on curved surfaces.

Partial local supersymmetry (N=(1,1) or N=(1,0)) suffices for these models to remain valid.

Coupling of N=(2,2) vector multiplets to N=(1,1) multiplets is successfully developed.

Abstract

We consider the effect of curved two-dimensional space-time on Witten's $N=2$ supersymmetric sigma models interpolating Calabi-Yau hypersurfaces to Landau-Ginzburg models. In order for the former models to have significant connection to superstring theory, only the $N=(1,1)$ or $N=(1,0)$ part of the total $N=(2,2)$ world-sheet supersymmetry is made local. Even though there arises an additional minimizing condition due to a scalar auxiliary field in the supergravity multiplet on curved two-dimensions, the essential feature of the sigma-model relating Calabi-Yau and Landau-Ginzburg models will be maintained. This indicates the validity of these sigma models formulated on curved two-dimensions or curved world-sheets. As a by-product, the coupling of $N=(2,2)$ vector multiplets to other multiplets with $N=(1,1)$ local supersymmetry is developed.