Generalized K\"ahler Geometry in (2,1) superspace

TL;DR

This paper explores the reduction of (2,2) supersymmetric sigma models to (2,1) superspace, revealing unique features and comparing quantization methods across formulations, thus deepening understanding of generalized K"ahler geometry.

Contribution

It provides a detailed analysis of the reduction process from (2,2) to (2,1) superspace and compares quantization approaches, highlighting new geometric insights.

Findings

Reduction from (2,2) to (2,1) involves nontrivial elimination of nondynamical fields.

Quantization methods differ across superspace formulations.

The study clarifies the geometric structure underlying supersymmetric sigma models.

Abstract

Two-dimensional (2,2) supersymmetric nonlinear sigma models can be described in (2,2), (2,1) or (1,1) superspaces. Each description emphasizes different aspects of generalized K\"ahler geometry. We investigate the reduction from (2,2) to (2,1) superspace. This has some interesting nontrivial features arising from the elimination of nondynamical fields. We compare quantization in the different superspace formulations.