Constraints on Automorphic Forms of Higher Derivative Terms from Compactification

TL;DR

This paper derives constraints on automorphic forms arising from higher derivative corrections in string and M-theory compactifications, linking them to specific E_{n+1} representations and string charges.

Contribution

It establishes a connection between higher derivative automorphic forms and fundamental E_{n+1} representations in compactified string and M-theory.

Findings

Automorphic forms involve the fundamental weight mbda^{n+1} of E_{n+1}.

String charges in d dimensions belong to the same representation.

Constraints are derived from dimensional reduction of higher derivative terms.

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 \lambda^{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.