Eisenstein series for infinite-dimensional U-duality groups

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.

69 pages. v2: Added references and small additions, to be published in JHEP

References in corpus (6)

• E7(7) constraints on counterterms in N=8 supergravity
• On duality symmetries of supergravity invariants
• E7(7) symmetry in perturbatively quantised N=8 supergravity
• Curvature corrections and Kac-Moody compatibility conditions
• Aspects of higher curvature terms and U-duality
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Cited by in corpus (14)

• Exotic Branes in String Theory
• Eisenstein series and automorphic representations
• Loops in exceptional field theory
• $D^6{R}^4$ amplitudes in various dimensions
• A master exceptional field theory
• Tetrahedral modular graph functions
• On supersymmetric E11 exceptional field theory
• Higher Derivative Supergravities in Diverse Dimensions
• Supergravity divergences, supersymmetry and automorphic forms
• Cancellation of divergences up to three loops in exceptional field theory
• On higher spin realizations of K(E10)
• $D^6{R}^4$ curvature corrections, modular graph functions and Poincaré series
• The E10 Wheeler-DeWitt operator at low levels
• Convergence of Kac--Moody Eisenstein Series over a function field