$R^4$ couplings and automorphic unipotent representations

Abstract

Four-graviton, eight-derivative couplings in the low energy effective action of toroidal type II string compactifications are tightly constrained by U-duality invariance and by supersymmetry. In this note, we revisit earlier proposals for the automorphic form governing these couplings in dimension D=3,4,5,6, and propose that the correct automorphic form is the minimal theta series for the corresponding U-duality group. Evidence for this proposal comes from i) the matching of infinitesimal characters, ii) the fact that the Fourier coefficients have support on 1/2-BPS charges and iii) decompactification limits. In particular, we show that non-perturbative effects can be interpreted as 1/2-BPS instantons, or 1/2-BPS particles in one dimension higher (together with Taub-NUT instantons in the D=3 case). Based on similar considerations, we also conjecture the form of 1/4-BPS saturated couplings such as ${\nabla }^4{R}^4$ couplings in the same dimensions.

30 pages; v2: new appendix on decompactification limits, and minor corrections, published version; v3: fixed various misprints

References in corpus (6)

• Automorphic properties of low energy string amplitudes in various dimensions
• Lectures on on Black Holes, Topological Strings and Quantum Attractors (2.0)
• D-instantons and twistors
• The D^4 R^4 term in type IIB string theory on T^2 and U-duality
• Minimal representations: spherical vectors and automorphic functionals
• Perturbation Theory From Automorphic Forms

Cited by in corpus (45)

• On the modular structure of the genus-one Type II superstring low energy expansion
• String theory dualities and supergravity divergences
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• Stringy KLT relations, global symmetries, and E_7(7) violation
• E7(7) symmetry in perturbatively quantised N=8 supergravity
• Multiparticle one-loop amplitudes and S-duality in closed superstring theory
• Small representations, string instantons, and Fourier modes of Eisenstein series (with an appendix by D. Ciubotaru and P. Trapa)
• Eisenstein series and automorphic representations
• Loops in exceptional field theory
• $D^6{R}^4$ amplitudes in various dimensions
• D-instantons, String Field Theory and Two Dimensional String Theory
• Normalization of Type IIB D-instanton Amplitudes
• Duality completion of higher derivative corrections
• Minimal unitary representations from supersymmetry
• Tetrahedral modular graph functions
• On supersymmetric E11 exceptional field theory
• The two D6R4 type invariants and their higher order generalisation
• Higher Derivative Supergravities in Diverse Dimensions
• Modular Forms and $SL(2,\mathbb{Z})$-covariance of type IIB superstring theory
• Species scale, worldsheet CFTs and emergent geometry
• Eisenstein series for infinite-dimensional U-duality groups
• Supergravity divergences, supersymmetry and automorphic forms
• Perturbation Theory From Automorphic Forms
• Infrared divergences and harmonic anomalies in the two-loop superstring effective action
• Constraints on Automorphic Forms of Higher Derivative Terms from Compactification
• Exact ${\nabla }^4{R}^4$ couplings and helicity supertraces
• Cancellation of divergences up to three loops in exceptional field theory
• Emergence of $R^4$-terms in M-theory
• Automorphic Instanton Partition Functions on Calabi-Yau Threefolds
• Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds
• Integral forms of Kac-Moody groups and Eisenstein series in low dimensional supergravity theories
• $D^6{R}^4$ curvature corrections, modular graph functions and Poincaré series
• 1/8-BPS Couplings and Exceptional Automorphic Functions
• Higher derivative type II string effective actions, automorphic forms and E11
• $\mathcal{E}{\nabla }^4{R}^4$ type invariants and their gradient expansion
• Perturbative higher-derivative terms in N=6 asymmetric orbifolds
• Parameters, limits and higher derivative type II string corrections
• Uniformization, Unipotent Flows and the Riemann Hypothesis
• On R^4 terms and MHV amplitudes in N = 5,6 supergravity vacua of Type II superstrings
• Fourier expansions of Kac-Moody Eisenstein series and degenerate Whittaker vectors
• Fourier coefficients attached to small automorphic representations of ${\mathrm{SL}}_n(\mathbb{A})$
• Poisson equations, higher derivative automorphic forms and string parameter limits
• Saturating unitarity bounds at U-duality symmetric points
• Symmetries of non-maximal supergravities with higher-derivative corrections
• Modular realizations of hyperbolic Weyl groups