A Kähler Structure on the Space of String World-Sheets
نویسنده
چکیده
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 infinitedimensional manifold S carries a natural complex structure and a compatible (positive-definite) Kähler metric h on S determined by the Lorentz metric g. Similar results are proved for other dimensions and signatures, thus generalizing results of Brylinski [2] regarding knots in 3-manifolds. Generalizing the framework of Lempert [5], we also investigate the precise sense in which S is an infinite-dimensional complex manifold. Running title: The Space of String World-Sheets ∗Supported in part by NSF grant DMS-92-04093.
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