The two D6R4 type invariants and their higher order generalisation

Abstract

We show that there are two distinct classes of D6R4 type supersymmetry invariants in maximal supergravity. The second class includes a coupling in F2D4R4 that generalises to 1/8 BPS protected F2kD4R4 couplings. We work out the supersymmetry constraints on the corresponding threshold functions, and argue that the functions in the second class satisfy to homogeneous differential equations for arbitrary k>0, such that the corresponding exact threshold functions in type II string theory should be proportional to Eisenstein series, which we identify. This analysis explains in particular that the exact D6R4 threshold function is the sum of an Eisenstein function and a solution to an inhomogeneous Poisson equation in string theory.

53 pages

References in corpus (11)

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Cited by in corpus (23)

• Loops in exceptional field theory
• Poisson equation for the Mercedes diagram in string theory at genus one
• Tetrahedral modular graph functions
• Poisson equation for the three loop ladder diagram in string theory at genus one
• Higher Derivative Supergravities in Diverse Dimensions
• Poincaré series for modular graph forms at depth two. I. Seeds and Laplace systems
• Supergravity divergences, supersymmetry and automorphic forms
• Infrared divergences and harmonic anomalies in the two-loop superstring effective action
• Exact ${\nabla }^4{R}^4$ couplings and helicity supertraces
• Supervertices and Non-renormalization Conditions in Maximal Supergravity Theories
• Cancellation of divergences up to three loops in exceptional field theory
• Low momentum expansion of one loop amplitudes in heterotic string theory
• To the cusp and back: Resurgent analysis for modular graph functions
• 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
• Perturbative higher-derivative terms in N=6 asymmetric orbifolds
• Non--analytic terms from nested divergences in maximal supergravity
• Fourier coefficients attached to small automorphic representations of ${\mathrm{SL}}_n(\mathbb{A})$
• Saturating unitarity bounds at U-duality symmetric points
• Worldsheet (anti)instanton bound states in type II on $T^2$
• Some finite terms from ladder diagrams in three and four loop maximal supergravity