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 E 9, E 10 and E 11. 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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Fleig, P., Kleinschmidt, A. Eisenstein series for infinite-dimensional U-duality groups. J. High Energ. Phys. 2012, 54 (2012). https://doi.org/10.1007/JHEP06(2012)054
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DOI: https://doi.org/10.1007/JHEP06(2012)054