English
 
User Manual Privacy Policy Disclaimer Contact us
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Paper

Elliptic modular graph forms I: Identities and generating series

MPS-Authors
/persons/resource/persons2677

Kleinschmidt,  Axel
Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

External Ressource
No external resources are shared
Fulltext (public)

2012.09198.pdf
(Preprint), 701KB

Supplementary Material (public)
There is no public supplementary material available
Citation

D'Hoker, E., Kleinschmidt, A., & Schlotterer, O. (in preparation). Elliptic modular graph forms I: Identities and generating series.


Cite as: http://hdl.handle.net/21.11116/0000-0007-CB80-3
Abstract
Elliptic modular graph functions and forms (eMGFs) are defined for arbitrary graphs as natural generalizations of modular graph functions and forms obtained by including the character of an Abelian group in their Kronecker--Eisenstein series. The simplest examples of eMGFs are given by the Green function for a massless scalar field on the torus and the Zagier single-valued elliptic polylogarithms. More complicated eMGFs are produced by the non-separating degeneration of a higher genus surface to a genus one surface with punctures. eMGFs may equivalently be represented by multiple integrals over the torus of combinations of coefficients of the Kronecker--Eisenstein series, and may be assembled into generating series. These relations are exploited to derive holomorphic subgraph reduction formulas, as well as algebraic and differential identities between eMGFs and their generating series.