Supergravity divergences, supersymmetry and automorphic forms

TL;DR

This paper explores divergences in maximal supergravity across dimensions, using supersymmetry constraints and automorphic forms to understand the structure of higher derivative couplings and their associated automorphic functions.

Contribution

It introduces a method employing tensorial differential equations to analyze U-duality invariant threshold functions and their automorphic properties in supergravity.

Findings

Automorphic functions linked to supergravity divergences are associated with special nilpotent orbits.

Fourier modes and wave-front sets of these functions are characterized in detail.

The approach reveals the structure of divergences through automorphic form analysis.

Abstract

We investigate the occurrence of divergences in maximal supergravity in various dimensions from the point of view of supersymmetry constraints on the U-duality invariant threshold functions defining the higher derivative couplings in the effective action. Our method makes use of tensorial differential equations that constrain these couplings. We study in detail the Fourier modes and wave-front sets of the associated automorphic functions and find that they are always associated to special nilpotent orbits.