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

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.Comment: 16 pages, Latex. Contribution to The 26th Winter School GEOMETRY AND PHYSICS, Czech Republic, Srni, January 14 - 21, 200

N=1 supersymmetric path-integral Poisson-Lie duality

We extend the path-integral formulation of Poisson-Lie duality found by Tyurin and von Unge to N=1 supersymmetric sigma-models. Using an explicit representation of the generators of the Drinfel'd double corresponding to GxU(1)^dimG we discuss an application to non-abelian duality. The paper also contains the relevant background and some comments on Poisson-Lie duality.Comment: 23 pages,latex2e,no figures;v2:minor corrections;v3:misprints corrected,final versio

2D supergravity in p+1 dimensions

We describe new $N$-extended 2D supergravities on a $(p+1)$-dimensional (bosonic) space. The fundamental objects are moving frame densities that equip each $(p+1)$-dimensional point with a 2D ``tangent space''. The theory is presented in a $[p+1, 2]$ superspace. For the special case of $p=1$ we recover the 2D supergravities in an unusual form. The formalism has been developed with applications to the string-parton picture of $D$-branes at strong coupling in mind.Comment: 16 pages, Late