Analytic fields on Riemann surfaces. II
type: Item
instance of: scholarly article
title: Analytic fields on Riemann surfaces. II
zbMATH Open document ID: 0656.58044
DOI: 10.1007/BF01225373
author: V. G. Knizhnik
published in: Communications in Mathematical Physics
publication date: 1987-01-01T00:00:00Z
review text: [For Part I see the preceding review Zbl 0656.58043.] The properties of analytic fields on a Riemann surface represented by a branch covering of \({\mathbb{C}}{\mathbb{P}}^ 1\) are investigated in detail. Branch points are shown to correspond to the vertex operators with simple conformal properties. As applications we compute determinants of \({\bar \partial}_ j\) operators for \(Z_ n\)-symmetric surfaces and obtain various representations for the two-loop measure in the bosonic string theory together with various identities for theta-functions of hyperelliptic surfaces. We also present an integral representation for the quantum part of the twist field correlation functions, which describe propagation of the string on the orbifold background. We also calculate the quantum part of the structure constants of the twist-field operator algebra, generalizing the results of Dixon, Friedan, Martinec, and Shenker.
Mathematics Subject Classification ID: 58Z05
Mathematics Subject Classification ID: 30F99
Mathematics Subject Classification ID: 53A30
Mathematics Subject Classification ID: 81T99
zbMATH DE Number: 4071989
zbMATH Keywords: analytic fields
zbMATH Keywords: Riemann surface
zbMATH Keywords: Branch points
zbMATH Keywords: vertex operators
zbMATH Keywords: bosonic string theory
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01225373
OpenAlex ID: W2034821556
description: scientific article; zbMATH DE number 4071989