Abstract
We show that Witten's open string diagrams are surfaces with metrics of minimal area under the condition that all nontrivial open Jordan curves be longer or equal to π. The minimal area property is used together with a mini-max problem to establish a new existence and uniqueness theorem for quadratic differentials in open Riemann surfaces with or without punctures on the boundaries. This theorem implies that the Feynman rules of open string theory give a single cover of the moduli of open Riemann surfaces.
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Communicated by S.-T. Yau
Supported in part by funds provided by the U.S. Department of Energy (D.O.E.) under contract #DE-AC02-76ER03069
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Zwiebach, B. A proof that Witten's open string theory gives a single cover of moduli space. Commun.Math. Phys. 142, 193–216 (1991). https://doi.org/10.1007/BF02099176
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DOI: https://doi.org/10.1007/BF02099176