Euclidean Supersymmetry, Twisting and Topological Sigma Models

TL;DR

This paper explores Euclidean N=2 supersymmetry, its R-symmetry structure, and the conditions for twisting and constructing topological sigma models, highlighting the need for complexification in certain cases.

Contribution

It clarifies the R-symmetry constraints in Euclidean N=2 supersymmetry and discusses the necessity of complexification for B-twists and models with H-flux.

Findings

A-twist is possible in Euclidean N=2 supersymmetry.

B-twist requires complexification of sigma models.

Obstructions exist for twisted chiral superfields in Euclidean superspace.

Abstract

We discuss two dimensional N-extended supersymmetry in Euclidean signature and its R-symmetry. For N=2, the R-symmetry is SO(2)\times SO(1,1), so that only an A-twist is possible. To formulate a B-twist, or to construct Euclidean N=2 models with H-flux so that the target geometry is generalised Kahler, it is necessary to work with a complexification of the sigma models. These issues are related to the obstructions to the existence of non-trivial twisted chiral superfields in Euclidean superspace.