Duality Groups, Automorphic Forms and Higher Derivative Corrections

Abstract

We study the higher derivative corrections that occur in type II superstring theories in ten dimensions or less. Assuming invariance under a discrete duality group G(Z) we show that the generic functions of the scalar fields that occur can be identified with automorphic forms. We then give a systematic method to construct automorphic forms from a given group G(Z) together with a chosen subgroup H and a linear representation of G(Z). This construction is based on the theory of non-linear realizations and we find that the automorphic forms contain the weights of G. We also carry out the dimensional reduction of the generic higher derivative corrections of the IIB theory to three dimensions and find that the weights of E_8 occur generalizing previous results of the authors on M-theory. Since the automorphic forms of this theory contain the weights of E_8 we can interpret the occurrence of weights in the dimensional reduction as evidence for an underlying U-duality symmetry.

Typos corrected and a reference added

References in corpus (7)

• Duality and higher derivative terms in M theory
• R^4, purified
• Higher order M theory corrections and the Kac-Moody algebra E10
• Enhanced Coset Symmetries and Higher Derivative Corrections
• Curvature corrections and Kac-Moody compatibility conditions
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• U-Duality and the Compactified Gauss-Bonnet Term
• Automorphic Instanton Partition Functions on Calabi-Yau Threefolds
• Arithmetic and Hyperbolic Structures in String Theory
• Higher derivative type II string effective actions, automorphic forms and E11
• Higher Derivative Corrections, Dimensional Reduction and Ehlers Duality
• Ehlers symmetry at the next derivative order
• Fourier expansions of Kac-Moody Eisenstein series and degenerate Whittaker vectors
• On the Geometry of Spacetime I: baby steps in quantum ring theory
• Symmetries of non-maximal supergravities with higher-derivative corrections