A Kahler structure on the space of string worldsheets

Details A Kahler structure on the space of string worldsheets A Kahler structure on the space of string worldsheets

Sep 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993cqgra..10l.141l&link_type=abstract

Classical and Quantum Gravity, Volume 10, Issue 9, pp. L141-L147 (1993).

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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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