Elsevier

Nuclear Physics B

Volume 294, 1987, Pages 556-572
Nuclear Physics B

The superstring, diff S1/S1, and holomorphic geometry

https://doi.org/10.1016/0550-3213(87)90597-9Get rights and content

Abstract

We incorporate superstrings into the non-perturbative formulation of string field theories based on Kähler geometry recently proposed by Bowick and Rajeev. The string field is conjectured to be the Kähler potential of loop space, its equation of motion given by the vanishing of the curvature of a product bundle constructed over a graded Diff S1/S1, as required for reparametrization invariance of the theory. We find that bosonic and fermionic loops in a Minkowski background solve the equation for the Kähler potential only in ten dimensions. We use geometric quantization techniques to calculate the curvature of the super-holomorphic vector bundle, since they emphasize the role of the complex geometry, and flag manifold techniques to calculate the curvature of the line bundle over super-Diff S1/S1.

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Work supported in part by the US Department of Energy under grant no. FG05-86-ER40272.

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