Abstract
It has been proposed that the string diagrams of closed string field theory be defined by a minimal area problem that requires that all nontrivial homotopy curves have length greater than or equal to 2π. Consistency requires that the minimal area metric be flat in a neighbourhood of the punctures. The theorem proven in this paper, yieds a criterion which if satisfied, will ensure this requirement. The theorem states roughly that the metric is flat in an open set,U if there is a unique closed curve of length 2π through every point inU and all of these closed curves are in the same free homotopy class.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
[SoZ] Sonoda, H., Zwiebach, B.: Closed string field theory loops with symmetric factorizable quadratic differentials. Nucl. Phys.B331, 592 (1990)
[Z1] Zwiebach, B.: How covariant closed string field theory solves a minimal area problem. Commun. Math. Phys.136, 83–118 (1991); Consistency of closed string polyhedra from minimal area. Phys. Lett.B241, 343 (1990)
[St] Strebel, K.: Quadratic differentials. Berlin, Heidelberg, New York: Springer 1984
[Z2] Zweibach, B.: Quantum closed strings from minimal area. Mod. Phys. Lett. A,5, No. 32, 2753 (1990)
[WZ] Wolf, M., Zwiebach, B.: Works in preparation
[A] Ahlfors, L. V.: Conformal invariants. McGraw-Hill Series in Higher Mathematics. New York: McGraw-Hill 1973
Author information
Authors and Affiliations
Additional information
Communicated by S.-T. Yau
Supported in part by funds provided by the US Department of Energy (DOE) under contract # DE-AC02-76ER03069
Rights and permissions
About this article
Cite this article
Ranganathan, K. A criterion for flatness in minimal area metrics that define string diagrams. Commun.Math. Phys. 146, 429–445 (1992). https://doi.org/10.1007/BF02097012
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02097012