The Mumford form and the Polyakov measure in string theory
type: Item
instance of: scholarly article
title: The Mumford form and the Polyakov measure in string theory
zbMATH Open document ID: 0604.14016
DOI: 10.1007/BF01220994
published in: Communications in Mathematical Physics
publication date: 1986-01-01T00:00:00Z
review text: The authors consider the moduli space \(M_ g\) of algebraic curves and obtain the Mumford form and the Polyakov measure on \(M_ g\) (for genus \(g\geq 2)\) by formulae written in terms of the complex geometry of the surface itself, instead of its spectral invariants. They compute the Polyakov measure by explicitly describing the Mumford form, a priori defined only by the implicit global conditions. They thus obtain a shorter formula than the one obtained by \textit{Yu. I. Manin} [JETP Lett. (USA) 43, No.4, 204-206 (1986); translation from Pis'ma Zh. Eksp. Teor. Fis. (USSR), 43, No.4, 161-163 (1986)]. They also obtain a new proof of a theorem of Mumford relative to sheaves associated with a family of smooth projective curves [\textit{D. Mumford}, Enseign. Math., II. Ser. 23, 39-110 (1977; Zbl 0363.14003)]. The authors also discuss the possibility of computing the Polyakov measure for the superstring in the critical dimension \(10\) by an intermediary Mumford-Berezin form on a suitable superalgebraic moduli space.
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 81T08
zbMATH DE Number: 3975083
zbMATH Keywords: moduli space of algebraic curves
zbMATH Keywords: Mumford form
zbMATH Keywords: Polyakov measure
zbMATH Keywords: superstring
zbMATH Keywords: superalgebraic moduli space
author: Alexander A. Beilinson
author: Yuri I. Manin
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3975083