Minimal unitary representations from supersymmetry

Abstract

We compute the supersymmetry constraints on the R^4 type corrections in maximal supergravity in dimension 8, 6, 4 and 3, and determine the tensorial differential equations satisfied by the function of the scalar fields multiplying the R^4 term in the corresponding invariants. The second order derivative of this function restricted to the Joseph ideal vanishes in dimension lower than six. These results are extended to the d^4 R^4 and the d^6 R^4 corrections, based on the harmonic superspace construction of these invariants in the linearised approximation. We discuss the solutions of these differential equations and analysis the consequences on the non-perturbative type II low energy string theory effective action.

84 pages, Corrected version for publication in JHEP, additional comment on d^6 R^4 in four dimensions

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Cited by in corpus (24)

• Eisenstein series and automorphic representations
• Loops in exceptional field theory
• $D^6{R}^4$ amplitudes in various dimensions
• Tetrahedral modular graph functions
• The two D6R4 type invariants and their higher order generalisation
• Higher Derivative Supergravities in Diverse Dimensions
• Supergravity divergences, supersymmetry and automorphic forms
• Infrared divergences and harmonic anomalies in the two-loop superstring effective action
• Supervertices and Non-renormalization Conditions in Maximal Supergravity Theories
• Exact ${\nabla }^4{R}^4$ couplings and helicity supertraces
• Cancellation of divergences up to three loops in exceptional field theory
• $D^6{R}^4$ curvature corrections, modular graph functions and Poincaré series
• 1/8-BPS Couplings and Exceptional Automorphic Functions
• $\mathcal{E}{\nabla }^4{R}^4$ type invariants and their gradient expansion
• Superforms in Five-Dimensional, $N=1$ Superspace
• Discrete anomalies in supergravity and consistency of string backgrounds
• Perturbative higher-derivative terms in N=6 asymmetric orbifolds
• Reductions of Exceptional Field Theories
• Fourier coefficients attached to small automorphic representations of ${\mathrm{SL}}_n(\mathbb{A})$
• Constraining non--BPS interactions from counterterms in three loop maximal supergravity
• 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
• Exotic Aspects of Extended Field Theories