Eisenstein Series in String Theory
High Energy Physics - Theory
2011-04-15 v2
Abstract
We discuss the relevance of Eisenstein series for representing certain G(Z)-invariant string theory amplitudes which receive corrections from BPS states only. The Eisenstein series are constructed using G(Z)-invariant mass formulae and are manifestly invariant modular functions on the symmetric space K\G(R) of non-compact type, with K the maximal compact subgroup of G(R). In particular, we show how Eisenstein series of the T-duality group SO(d,d,Z) can be used to represent one- and g-loop amplitudes in compactified string theory. We also obtain their non-perturbative extensions in terms of the Eisenstein series of the U-duality group E_{d+1(d+1)}(Z).
Cite
@article{arxiv.hep-th/9910115,
title = {Eisenstein Series in String Theory},
author = {N. A. Obers and B. Pioline},
journal= {arXiv preprint arXiv:hep-th/9910115},
year = {2011}
}
Comments
11 pages, Latex, submitted to Proceedings of Strings '99, published version