Duality Groups, Automorphic Forms and Higher Derivative Corrections

Details Duality Groups, Automorphic Forms and Higher Derivative Corrections Duality Groups, Automorphic Forms and Higher Derivative Corrections

2006-11-29

arxiv.org/abs/hep-th/0611318v2

Phys.Rev.D75:066002,2007

Physics

High Energy Physics

High Energy Physics - Theory

Typos corrected and a reference added

Scientific paper

10.1103/PhysRevD.75.066002

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.

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