Supersymmetric Sigma Model geometry

TL;DR

This paper reviews how superspace sigma models are powerful tools for exploring complex geometries, including hyperk"ahler and generalized K"ahler structures, with emphasis on various reduction and construction techniques.

Contribution

It provides a comprehensive overview of superspace sigma models and introduces new methods for constructing hyperk"ahler and generalized K"ahler geometries.

Findings

Hyperk"ahler reduction techniques explained

Projective superspace methods detailed

New constructions of hyperk"ahler metrics on symmetric spaces

Abstract

This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyper)k\"ahler reduction; projective superspace; the generalized Legendre construction; generalized K\"ahler geometry and constructions of hyperk\"ahler metrics on Hermitean symmetric spaces.