Haploid (2,2)-Superfields In 2-Dimensional Spacetime

TL;DR

This paper explores a class of superfields in 2D (2,2)-superspace that are independent of half the fermionic coordinates, revealing a broader class of target space geometries than traditionally considered for supersymmetric theories.

Contribution

It introduces and analyzes haploid (2,2)-superfields in 2D superspace, expanding the understanding of possible target space geometries beyond Kahler manifolds.

Findings

Identifies a broad class of superfields with potential for richer geometries.

Constructs a general Lagrangian under certain restrictions.

Shows these geometries are more general than Kahler manifolds.

Abstract

Superfields in 2-dimensional (2,2)-superspacetime which are independent of (some) half of the fermionic coordinates are discussed in a hopefully both comprehensive and comprehensible manner. An embarrassing abundance of these simplest `building blocks' makes it utterly impossible to write down the `most general Lagrangian'. With some ad hoc but perhaps plausible restrictions, a rather general Lagrangian is found, which exhibits many of the phenomena that have been studied recently, and harbors many more. In particular, it becomes patently obvious that the (2,2)-supersymmetric 2-dimensional field theory target space geometries (many of which are suitable for (super)string propagation) are far more general than Kahler manifolds with holomorphic bundles.