Dimensionally reduced gravity,Hermitian symmetric spaces andtheAshtekar variables

Abstract

Dimensional reductions of various higher-dimensional (super)gravitytheories lead toeffectively two-dimensional field theories described by gravity-coupledG/H nonlinear σ-models. We show that a new set ofcomplexifiedvariablescan be introduced when G/H is aHermitian symmetric space.This generalizes an earlier construction that grew out of the Ashtekarformulation of two-Killing-vector reduced pure four-dimensional generalrelativity.Apart from givingsome new insights into dimensional reductions of higher-dimensional(super)gravity theories, these Ashtekar-type variablesoffer several technical advantages in the context of the exactquantization of these models. As an application, an infiniteset of conserved charges is constructed. Our results might serve as astarting point for probing the quantum equivalence of theAshtekar and the metric formalism within a non-trivial midi-superspacemodel of quantum gravity.