TY  - JOUR
AU  - Ninnemann, Holger
TI  - Deformations of super Riemann surfaces
JO  - Communications in mathematical physics
VL  - 150
IS  - 2
SN  - 1432-0916
CY  - Berlin
PB  - Springer
M1  - PUBDB-2017-09092
SP  - 267 - 288
PY  - 1992
N1  - Theorie
AB  - Two different approaches to (Kostant-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 Poincaré upper half-plane provides a simple description of super Laplace operators acting on automorphicp-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.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:A1992KA32300003
DO  - DOI:10.1007/BF02096661
UR  - https://bib-pubdb1.desy.de/record/389862
ER  -