Communications in Mathematical Physics

, Volume 142, Issue 1, pp 193–216 | Cite as

A proof that Witten's open string theory gives a single cover of moduli space

  • Barton Zwiebach


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.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Modulus Space 
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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Barton Zwiebach
    • 1
  1. 1.Center for Theoretical Physics, Laboratory for Nuclear Science and Department of PhysicsMassachusetts Institute of TechnologyCambridgeUSA

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