Eisenstein Series in String Theory

Details Eisenstein Series in String Theory Eisenstein Series in String Theory

1999-10-15

arxiv.org/abs/hep-th/9910115v2

Class.Quant.Grav.17:1215-1224,2000

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, Latex, submitted to Proceedings of Strings '99, published version

Scientific paper

10.1088/0264-9381/17/5/330

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).

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