A brief review of supersymmetric non-linear sigma models and generalized complex geometry

Abstract

This is a review of the relation between supersymmetric non-linear sigma models and target space geometry. In particular, we report on the derivation of generalized K\"ahler geometry from sigma models with additional spinorial superfields. Some of the results reviewed are: Generalized complex geometry from sigma models in the Lagrangian formulation; Coordinatization of generalized K\"ahler geometry in terms of chiral, twisted chiral and semi-chiral superfields; Generalized K\"ahler geometry from sigma models in the Hamiltonian formulation.