Dimensionally Reduced Gravity, Hermitian Symmetric Spaces and the Ashtekar Variables

Details Dimensionally Reduced Gravity, Hermitian Symmetric Spaces and the Ashtekar Variables Dimensionally Reduced Gravity, Hermitian Symmetric Spaces and the Ashtekar Variables

1999-11-29

arxiv.org/abs/gr-qc/9911118v1

Class.Quant.Grav. 17 (2000) 2749-2764

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

20 pages, no figures, Latex2e

Scientific paper

10.1088/0264-9381/17/14/310

Dimensional reductions of various higher dimensional (super)gravity theories lead to effectively two-dimensional field theories described by gravity coupled G/H nonlinear sigma-models. We show that a new set of complexified variables can be introduced when G/H is a Hermitian symmetric space. This generalizes an earlier construction that grew out of the Ashtekar formulation of two Killing vector reduced pure 4d general relativity. Apart from giving some new insights into dimensional reductions of higher dimensional (super)gravity theories, these Ashtekar-type variables offer several technical advantages in the context of the exact quantization of these models. As an application, an infinite set of conserved charges is constructed. Our results might serve as a starting point for probing the quantum equivalence of the Ashtekar and the metric formalism within a non-trivial midi-superspace model of quantum gravity.

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