Constraints on Automorphic Forms of Higher Derivative Terms from Compactification

Abstract

By dimensionally reducing the higher derivative corrections of ten-dimensional IIB theory on a torus we deduce constraints on the E_{n+1} automorphic forms that occur in d=10-n dimensions. In particular we argue that these automorphic forms involve the representation of E_{n+1} with fundamental weight λ^{n+1}, which is also the representation to which the string charges in d dimensions belong. We also consider a similar calculation for the reduction of higher derivative terms in eleven-dimensional M-theory.

Minor corrections, to appear in JHEP

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• E_11 and M Theory
• E10 and a "small tension expansion" of M Theory
• Duality and higher derivative terms in M theory
• Two loops in eleven dimensions
• Automorphic properties of low energy string amplitudes in various dimensions
• Kac-Moody Symmetries of IIB Supergravity
• Non-renormalisation Conditions in Type II String Theory and Maximal Supergravity
• New Higher-Derivative $R^4$ Theorems
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• Duality Groups, Automorphic Forms and Higher Derivative Corrections
• Aspects of higher curvature terms and U-duality
• The D^{10} R^4 term in type IIB string theory
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Cited by in corpus (12)

• Small representations, string instantons, and Fourier modes of Eisenstein series (with an appendix by D. Ciubotaru and P. Trapa)
• Eisenstein series and automorphic representations
• Eisenstein series for infinite-dimensional U-duality groups
• Perturbation Theory From Automorphic Forms
• Integral forms of Kac-Moody groups and Eisenstein series in low dimensional supergravity theories
• $D^6{R}^4$ curvature corrections, modular graph functions and Poincaré series
• Higher derivative type II string effective actions, automorphic forms and E11
• Uniformization, Unipotent Flows and the Riemann Hypothesis
• Parameters, limits and higher derivative type II string corrections
• Fourier expansions of Kac-Moody Eisenstein series and degenerate Whittaker vectors
• Poisson equations, higher derivative automorphic forms and string parameter limits
• Kac--Moody groups and automorphic forms in low dimensional supergravity theories