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Journal Article

Eisenstein series for infinite-dimensional U-duality groups


Fleig,  Philipp
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE;


Kleinschmidt,  Axel
Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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Fleig, P., & Kleinschmidt, A. (2012). Eisenstein series for infinite-dimensional U-duality groups. Journal of High Energy Physics, 2012(06): 054. Retrieved from http://arxiv.org/abs/1204.3043.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-870B-3
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.