Dimensionally reduced gravity, Hermitian symmetric spaces and the Ashtekarvariables

Dimensional reductions of various higher-dimensional (super)gravity theorie s lead to effectively two-dimensional field theories described by gravity-c oupled G/H nonlinear sigma-models. We show that a new set of complexified v ariables can be introduced when G/H is a Hermitian symmetric space. This ge neralizes an earlier construction that grew out of the Ashtekar formulation of two-Killing-vector reduced pure four-dimensional general relativity. Ap art from giving some new insights into dimensional reductions of higher-dim ensional (super)gravity theories, these Ashtekar-type variables offer sever al technical advantages in the context of the exact quantization of these m odels. As an application, an infinite set of conserved charges is construct ed. Our results might serve as a starting point for probing the quantum equ ivalence of the Ashtekar and the metric formalism within a non-trivial midi -superspace model of quantum gravity.