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arXiv · hep-th/9910115

Eisenstein Series in String Theory

N. A. Obers·B. Pioline
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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).

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N. A. Obers, B. Pioline. 2000-03-01. Eisenstein Series in String Theory. https://doi.org/10.1088/0264-9381%2F17%2F5%2F330

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