Supersymmetry, R-symmetry, and positivity constrain planar 4d EFTs to match the open string Veneziano amplitude at tree level.
SUSY Ward identities, Superamplitudes, and Counterterms
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abstract
Ward identities of SUSY and R-symmetry relate n-point amplitudes in supersymmetric theories. We review recent work in which these Ward identities are solved in N=4 SYM and N=8 supergravity. The solution, valid at both tree and loop level, expresses any (Next-to)^K MHV superamplitude in terms of a basis of ordinary amplitudes. Basis amplitudes are classified by semi-standard tableaux of rectangular N-by-K Young diagrams. The SUSY Ward identities also impose constraints on the matrix elements of candidate ultraviolet counterterms in N=8 supergravity, and they can be studied using superamplitude basis expansions. This leads to a novel and quite comprehensive matrix element approach to counterterms, which we also review. This article is an invited review for a special issue of Journal of Physics A devoted to "Scattering Amplitudes in Gauge Theories".
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hep-th 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
In planar N=4 SYM the IR-finite hard amplitude satisfies an uncorrected tree-level soft theorem and represents the undeformed tree-level S-algebra of soft gluons.
citing papers explorer
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String Theory from Maximal Supersymmetry
Supersymmetry, R-symmetry, and positivity constrain planar 4d EFTs to match the open string Veneziano amplitude at tree level.
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Soft Algebra for ${\cal N}=4$ SYM
In planar N=4 SYM the IR-finite hard amplitude satisfies an uncorrected tree-level soft theorem and represents the undeformed tree-level S-algebra of soft gluons.