Supergravity divergences, supersymmetry and automorphic forms

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.

45 pages, 2 figures. v2: JHEP version with small corrections

References in corpus (5)

• Universal BPS structure of stationary supergravity solutions
• Matching the $D^6{\mathcal{R}}^4$ interaction at two-loops
• $D^6{R}^4$ amplitudes in various dimensions
• Minimal unitary representations from supersymmetry
• The two D6R4 type invariants and their higher order generalisation

Cited by in corpus (15)

• Eisenstein series and automorphic representations
• Loops in exceptional field theory
• Poisson equation for the Mercedes diagram in string theory at genus one
• Higher Derivative Supergravities in Diverse Dimensions
• Poisson equation for the three loop ladder diagram in string theory at genus one
• Infrared divergences and harmonic anomalies in the two-loop superstring effective action
• Cancellation of divergences up to three loops in exceptional field theory
• Supersymmetry Constraints and String Theory on K3
• $D^6{R}^4$ curvature corrections, modular graph functions and Poincaré series
• 1/8-BPS Couplings and Exceptional Automorphic Functions
• Perturbative type II amplitudes for BPS interactions
• String theory integrands and supergravity divergences
• Non--analytic terms from nested divergences in maximal supergravity
• Saturating unitarity bounds at U-duality symmetric points
• Symmetries of non-maximal supergravities with higher-derivative corrections