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arXiv · 1204.3043

Eisenstein series for infinite-dimensional U-duality groups

Philipp Fleig·Axel Kleinschmidt
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Abstract

We consider Eisenstein series appearing as coefficients of curvature corrections in the low-energy expansion of type II string theory four-graviton scattering amplitudes. We define these Eisenstein series over all groups in the E_n series of string duality groups, and in particular for the infinite-dimensional Kac-Moody groups E9, E10 and E11. We show that, remarkably, the so-called constant term of Kac-Moody-Eisenstein series contains only a finite number of terms for particular choices of a parameter appearing in the definition of the series. This resonates with the idea that the constant term of the Eisenstein series encodes perturbative string corrections in BPS-protected sectors allowing only a finite number of corrections. We underpin our findings with an extensive discussion of physical degeneration limits in D<3 space-time dimensions.

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Philipp Fleig, Axel Kleinschmidt. 2012-04-13. Eisenstein series for infinite-dimensional U-duality groups. https://doi.org/10.1007/jhep06(2012)054

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