$D^6{R}^4$ amplitudes in various dimensions

Abstract

Four-graviton couplings in the low energy effective action of type II string vacua compactified on tori are strongly constrained by supersymmetry and U-duality. While the $R^4$ and $D^4{R}^4$ couplings are known exactly in terms of Langlands-Eisenstein series of the U-duality group, the $D^6{R}^4$ couplings are not nearly as well understood. Exploiting the coincidence of the U-duality group in $D=6$ with the T-duality group in $D=5$, we propose an exact formula for the $D^6{R}^4$ couplings in type II string theory compactified on $T^4$, in terms of a genus-two modular integral plus a suitable Eisenstein series. The same modular integral computes the two-loop correction to $D^6{R}^4$ in 5 dimensions, but here provides the non-perturbative completion of the known perturbative terms in $D=6$. This proposal hinges on a systematic re-analysis of the weak coupling and large radius of the $D^6{R}^4$ in all dimensions $D\ge 3$, which fills in some gaps and resolves some inconsistencies in earlier studies.

18 pages (+ 26 page appendix), three Mathematica files included with submission; v2: minor corrections, version to appear in JHEP

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Cited by in corpus (31)

• On the modular structure of the genus-one Type II superstring low energy expansion
• Where is String Theory?
• The M-Theory S-Matrix From ABJM: Beyond 11D Supergravity
• Eisenstein series and automorphic representations
• AdS${}_4$/CFT${}_3$ from Weak to Strong String Coupling
• Loops in exceptional field theory
• Poisson equation for the Mercedes diagram in string theory at genus one
• Constraining Higher Derivative Supergravity with Scattering Amplitudes
• D-instantons, String Field Theory and Two Dimensional String Theory
• Normalization of Type IIB D-instanton Amplitudes
• D-instantons in Type IIA string theory on Calabi-Yau threefolds
• Tetrahedral modular graph functions
• On supersymmetric E11 exceptional field theory
• The two D6R4 type invariants and their higher order generalisation
• Where is M-theory in the space of scattering amplitudes?
• Higher Derivative Supergravities in Diverse Dimensions
• Poisson equation for the three loop ladder diagram in string theory at genus one
• Supergravity divergences, supersymmetry and automorphic forms
• Poincaré series for modular graph forms at depth two. I. Seeds and Laplace systems
• Infrared divergences and harmonic anomalies in the two-loop superstring effective action
• Exact ${\nabla }^4{R}^4$ couplings and helicity supertraces
• 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
• $D^6{R}^4$ curvature corrections, modular graph functions and Poincaré series
• 1/8-BPS Couplings and Exceptional Automorphic Functions
• Perturbative type II amplitudes for BPS interactions
• Hierarchy of Modular Graph Identities
• String theory integrands and supergravity divergences
• Non--analytic terms from nested divergences in maximal supergravity
• Worldsheet (anti)instanton bound states in type II on $T^2$