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Deformations of super Riemann surfaces

Journal Article:

Abstract

Two different approaches to (Konstant-Leites-) super Riemann surfaces are investigated. In the local approach, i.e. glueing open superdomains by superconformal transition functions, deformations of the superconformal structure are discussed. On the other hand, the representation of compact super Riemann surfaces of genus greater than one as a fundamental domain in the Poincare upper half-plane provides a simple description of super Laplace operators acting on automorphic p-forms. Considering purely odd deformations of super Riemann surfaces, the number of linear independent holomorphic sections of arbitrary holomorphic line bundles will be shown to be independent of the odd moduli, leading to a simple proof of the Riemann-Roch theorem for compact super Riemann surfaces. As a further consequence, the explicit connections between determinants of super Laplacians and Selberg's super zeta functions can be determined, allowing to calculate at least the 2-loop contribution to the fermionic string partition function. (orig.).
Authors:
Ninnemann, H [1] 
  1. Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
Publication Date:
Nov 01, 1992
Product Type:
Journal Article
Reference Number:
DEN-92-013387; EDB-93-005025
Resource Relation:
Journal Name: Communications in Mathematical Physics; (Germany); Journal Volume: 150:2
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; SUPERSYMMETRY; RIEMANN SPACE; ACTION INTEGRAL; COMMUTATION RELATIONS; COMMUTATORS; CONFORMAL INVARIANCE; CONFORMAL MAPPING; DEFORMATION; DIFFERENTIAL GEOMETRY; FERMIONS; FIELD OPERATORS; GRADED LIE GROUPS; INTEGRAL CALCULUS; LAGRANGIAN FIELD THEORY; LAPLACIAN; LOCALITY; PARTITION FUNCTIONS; RIEMANN FUNCTION; SMOOTH MANIFOLDS; SPACE-TIME; SPINOR FIELDS; SUPERSTRING MODELS; TOPOLOGY; TRAJECTORIES; COMPOSITE MODELS; EXTENDED PARTICLE MODEL; FIELD THEORIES; FUNCTIONS; GEOMETRY; INTEGRALS; INVARIANCE PRINCIPLES; LIE GROUPS; MAPPING; MATHEMATICAL MANIFOLDS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; MATHEMATICAL SPACE; MATHEMATICS; PARTICLE MODELS; QUANTUM FIELD THEORY; QUANTUM OPERATORS; QUARK MODEL; SPACE; STRING MODELS; SYMMETRY; SYMMETRY GROUPS; TOPOLOGICAL MAPPING; TRANSFORMATIONS; 662120* - General Theory of Particles & Fields- Symmetry, Conservation Laws, Currents & Their Properties- (1992-)
OSTI ID:
7174517
Country of Origin:
Germany
Language:
English
Other Identifying Numbers:
Journal ID: ISSN 0010-3616; CODEN: CMPHAY
Submitting Site:
DEN
Size:
Pages: 267-288
Announcement Date:
Jan 01, 1993

Journal Article:

Citation Formats

Ninnemann, H. Deformations of super Riemann surfaces. Germany: N. p., 1992. Web. doi:10.1007/BF02096661.
Ninnemann, H. Deformations of super Riemann surfaces. Germany. doi:10.1007/BF02096661.
Ninnemann, H. 1992. "Deformations of super Riemann surfaces." Germany. doi:10.1007/BF02096661. https://www.osti.gov/servlets/purl/10.1007/BF02096661.
@misc{etde_7174517,
title = {Deformations of super Riemann surfaces}
author = {Ninnemann, H}
abstractNote = {Two different approaches to (Konstant-Leites-) super Riemann surfaces are investigated. In the local approach, i.e. glueing open superdomains by superconformal transition functions, deformations of the superconformal structure are discussed. On the other hand, the representation of compact super Riemann surfaces of genus greater than one as a fundamental domain in the Poincare upper half-plane provides a simple description of super Laplace operators acting on automorphic p-forms. Considering purely odd deformations of super Riemann surfaces, the number of linear independent holomorphic sections of arbitrary holomorphic line bundles will be shown to be independent of the odd moduli, leading to a simple proof of the Riemann-Roch theorem for compact super Riemann surfaces. As a further consequence, the explicit connections between determinants of super Laplacians and Selberg's super zeta functions can be determined, allowing to calculate at least the 2-loop contribution to the fermionic string partition function. (orig.).}
doi = {10.1007/BF02096661}
journal = {Communications in Mathematical Physics; (Germany)}
volume = {150:2}
journal type = {AC}
place = {Germany}
year = {1992}
month = {Nov}
}