A brief review of supersymmetric non-linear sigma models and generalized complex geometry. (English) Zbl 1164.53400

Lindström, Ulf

Arch. Math., Brno 42, No. 5, 307-318 (2006).

Summary: 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 Kähler 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 Kähler geometry in terms of chiral, twisted chiral and semi-chiral superfields; Generalized Kähler geometry from sigma models in the Hamiltonian formulation.

MSC:

53C80	Applications of global differential geometry to the sciences
81T60	Supersymmetric field theories in quantum mechanics

Keywords:

sigma model; generalized Kähler geometry; generalized complex geometry; superfield