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String equations of motion from vanishing curvature. (English) Zbl 0746.53054

The geometric quantization of the closed bosonic string naturally leads to the identification of the space of all complex structures with the manifold \(M=\text{Diff} S^ 1/S^ 1\) associated with the space of loops in a certain classical background. In an earlier paper [the first author and S. G. Rajeev, Nucl. Phys. B 293, 348-384 (1987)] the Einstein equations were obtained in the adiabatic approximation from the requirement of the vanishing of the curvature of the tensor product of certain vector bundles over \(M\). This approach is extended in the present paper to include all the massless modes of the closed bosonic string, i.e. the graviton, antisymmetric tensor field and dilaton.
Reviewer: H.Rumpf (Wien)

MSC:

53Z05 Applications of differential geometry to physics
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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