Poisson equations, higher derivative automorphic forms and string parameter limits

Abstract

This paper considers the higher derivative terms in the effective action of type II string theory and in particular the behaviour of the automorphic forms they contain in all the different possible limits of the string parameters. The automorphic forms are thought to obey Poisson equations which contain the Laplacian defined on the coset space to which the scalars fields belong and we compute this Laplacian in all the possible string theory limits. We also consider these Poisson equations in the decompactification limit of a single dimension and by making two assumptions, one on the generic form of this equation and the other on the behaviour of the automorphic forms in this limit, we find strong constraints on the allowed form of this differential equation. We show that these constraints allow one to recover much of what was previously known about the automorphic forms corresponding to terms in the effective action that have fourteen or fewer space-time derivatives in a simple way.

47 pages, references added and typos corrected

References in corpus (5)

• The D^4 R^4 term in type IIB string theory on T^2 and U-duality
• Modular properties of two-loop maximal supergravity and connections with string theory
• The D^{10} R^4 term in type IIB string theory
• The structure of the R^8 term in type IIB string theory
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Cited by in corpus (2)

• The D^6 R^4 term from three loop maximal supergravity
• Constraining non--BPS interactions from counterterms in three loop maximal supergravity