A Kaehler Structure on the Space of String World-Sheets

Details A Kaehler Structure on the Space of String World-Sheets A Kaehler Structure on the Space of String World-Sheets

1993-05-26

arxiv.org/abs/alg-geom/9305012v1

Mathematics

Algebraic Geometry

13 pages, LaTeX

Scientific paper

10.1088/0264-9381/10/9/006

Let (M,g) be an oriented Lorentzian 4-manifold, and consider the space S of oriented, unparameterized time-like 2-surfaces in M (string world-sheets) with fixed boundary conditions. Then the infinite-dimensional manifold S carries a natural complex structure and a compatible (positive-definite) Kaehler metric h on S determined by the Lorentz metric g. Similar results are proved for other dimensions and signatures, thus generalizing results of Brylinski regarding knots in 3-manifolds. Generalizing the framework of Lempert, we also investigate the precise sense in which S is an infinite-dimensional complex manifold.

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