Teichmüller spaces of string theory
type: Item
instance of: scholarly article
title: Teichmüller spaces of string theory
zbMATH Open document ID: 0790.32023
DOI: 10.1007/BF00675198
published in: International Journal of Theoretical Physics
publication date: 1993-11-30T00:00:00Z
review text: The author gives a rigorous mathematical analysis of string theory. In Section 2 he shows for a Lorentzian world sheet swept by a string propagation in \(\mathbb{R}^{I,D}\) that a one-parameter family of conformally equivalent Riemann structures on the sheet forms an infinite geodesic in the appropriate Teichmüller space, the so called \(P\)-line. In Section 3 the author investigates the harmonic \(P\)-lines which are induced by harmonic homothetic Gauss maps. Considering Bers embedding of the Teichmüller space to the Banach space of bounded quadratic differentials the author shows in Section 4 that if the \(P\)-line relates to a quadratic differential of Jenkins-Strebel type (i.e. holomorphic quadratic differential that has closed horizontal and vertical trajectories) then endpoints of the \(P\)-line are represented by boundary points of that embedding and that leads to the decomposition of the world sheet onto one or more Riemann surfaces. In physical language it means that the \(P\)-lines corresponding to Jenkins-Strebel differentials describes world sheet which has to be created and to decay. In Section 5 the author proves that if the Jenkins-Strebel differential determining the \(P\)-line has only one horizontal and vertical cylinder of the same heights and circumferences then the space-time has to be discrete. At last in Section 6 the author introduces in Teichmüller space the global Fenchel-Nielsen coordinates and shows that the \(P\)-line corresponding to the Jenkins-Strebel differentials with \(3p-3\) cylinders \((p\) is a genus) can be related to a Hamiltonian system with respect to the Weil- Petersson-Kähler symplectic form.
Mathematics Subject Classification ID: 32G81
Mathematics Subject Classification ID: 32G15
Mathematics Subject Classification ID: 81T30
Mathematics Subject Classification ID: 30F30
Mathematics Subject Classification ID: 30F60
zbMATH DE Number: 445105
zbMATH Keywords: string theory
zbMATH Keywords: Teichmüller space
zbMATH Keywords: Bers embedding
zbMATH Keywords: quadratic differentials
zbMATH Keywords: Riemann surfaces
zbMATH Keywords: Jenkins-Strebel
zbMATH Keywords: space-time
zbMATH Keywords: Fenchel- Nielsen coordinates
zbMATH Keywords: Hamiltonian
zbMATH Keywords: Weil-Petersson-Kähler symplectic form
author: Krystyna Bugajska
reviewed by: E. D. Belokolos
MaRDI profile type: Publication
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Wikidata QID: Q126089916
full work available at URL: https://doi.org/10.1007/bf00675198
OpenAlex ID: W2067205372
description: scientific article; zbMATH DE number 445105