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Flattening of the EFT-Hedron: Supersymmetric Positivity Bounds and the Search for String Theory
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abstract
We examine universal positivity constraints on $2 \to 2$ scattering in 4d planar $N=4$ supersymmetric Yang-Mills theory with higher-derivative corrections. We present numerical evidence that the convex region of allowed Wilson coefficients (the ``EFT-hedron'') flattens completely along about one-third of its dimensions when an increasing number of constraints on the spectral density from crossing-symmetry are included. Our analysis relies on the formulation of the positivity constraints as a linear optimization problem, which we implement using two numerical solvers, SDPB and CPLEX. Motivated by the flattening, we propose a novel partially resummed low-energy expansion of the $2 \to 2$ amplitude. As part of the analysis, we provide additional evidence in favor of the conjecture [1] that the Veneziano amplitude is the only amplitude compatible with both S-matrix bootstrap constraints and string monodromy.
Forward citations
Cited by 7 Pith papers
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String Theory from Maximal Supersymmetry
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Strings from Almost Nothing
Ultrasoft, minimally structured scattering amplitudes are forced onto the Veneziano and Virasoro-Shapiro amplitudes of string theory.
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Splitting Regions and Shrinking Islands from Higher Point Constraints
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Worldsheet for Generalized Veneziano Amplitudes
A chiral composite linear dilaton worldsheet action reproduces Mandelstam's generalized Veneziano amplitudes and yields new partially crossing-symmetric higher-point and closed-string amplitudes.
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Bootstrapping Gravity with Crossing Symmetric Dispersion Relations
A crossing-symmetric dispersion-relation bootstrap reproduces known gravitational EFT bounds and gives new tree-level limits on the graviton coupling to a massive spin-4 state.
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