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Where is String Theory?
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abstract
We use the S-matrix bootstrap to carve out the space of unitary, crossing symmetric and supersymmetric graviton scattering amplitudes in ten dimensions. We focus on the leading Wilson coefficient $\alpha$ controlling the leading correction to maximal supergravity. The negative region $\alpha<0$ is excluded by a simple dual argument based on linearized unitarity (the desert). A whole semi-infinite region $\alpha \gtrsim 0.14$ is allowed by the primal bootstrap (the garden). A finite intermediate region is excluded by non-perturbative unitarity (the swamp). Remarkably, string theory seems to cover all (or at least almost all) the garden from very large positive $\alpha$ -- at weak coupling -- to the swamp boundary -- at strong coupling.
Forward citations
Cited by 18 Pith papers
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Partial Waves for Multipositivity
The paper constructs kinematic charts and partial-wave expansions for four-, five-, and six-point massless planar amplitudes tailored to multipositivity bounds.
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Unitary Dual-Resonance S-matrices
Smearing Veneziano blocks over continuous Regge slopes yields local, analytic, crossing-symmetric S-matrices with full partial-wave unitarity and controllable second-sheet resonances.
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Geometry of effective field theory positivity cones
For three particle flavors, the positivity cone C_W has exactly three families of extremal rays, one of which yields genuinely new inelastic constraints not implied by elastic bounds.
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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
Imposing 5-point split conditions and unitarity bounds selects the string beta function as the unique 4-point amplitude, up to equal-mass infinite spin towers.
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Scalar weak gravity bound from full unitarity
For a shift-symmetric scalar EFT with gravity, unitarity and dispersion relations imply Λ/M_P < 2.38 \tilde{g}_2^{1/5} and, in an improved smeared version, Λ^2/M_P^2 < 0.0115 |\tilde{g}_2|.
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The EFT Bootstrap at Finite $M_{PL}$
One-loop gravity effects make forward-limit positivity bounds ill-defined for massless scalar-gravity EFTs, forcing non-forward dispersion relations that shift the tree-level bounds by order-one factors.
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The Double EFT Expansion in Quantum Gravity
Quantum gravity EFT actions organize higher-curvature corrections into a field-theoretic expansion suppressed by the lightest new mass and a quantum-gravitational expansion suppressed by the species scale.
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Running EFT-hedron with null constraints at loop level
One-loop massless corrections modify the null constraints of shift-symmetric scalar EFTs, and IR-finite combinations of them reproduce tree-level bounds in the weak-coupling limit while deforming bounds in five and si...
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Bootstrapping Extremal Scalar Amplitudes With and Without Supersymmetry
The full space of allowed four-point scalar amplitudes is conjectured to be the convex hull of a single scalar amplitude and a one-parameter family of extremal theories, generatable from maximally supersymmetric amplitudes.
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The S-matrix bootstrap with neural optimizers I: zero double discontinuity
A neural optimizer solves the Atkinson-Mandelstam unitarity equations over the full space of amplitudes and, together with standard bootstrap methods, maps the allowed region of zero-double-discontinuity S-matrices, t...
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Bootstrapping leading hadronic muon anomaly
Bootstrap constraints plus QCD sum rules give a lower bound on the hadronic muon anomaly and an emergent rho-meson peak.
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Matrix moment approach to positivity bounds and UV reconstruction from IR
Positivity bounds for multi-field EFTs are formulated as matrix moment problems, yielding optimal bounds and a method to reverse engineer the UV mass, spin, and coupling spectrum from low-energy coefficients.
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Higher-Spin and Higher-Point Constraints on Stringy Amplitudes
Factorization at the second excited mass level forces the Regge intercept to the bosonic string value, and large-level multipositivity bounds forbid the simplest Gross satellite deformation of four-point superstring a...
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A glimpse into the Ultrametric spectrum
Quantum oscillators with energies from the Vladimirov derivative on the p-adic unit circle — exponentially spaced and exponentially degenerate — give string-like square-root-of-energy entropy, modulated by log-periodi...
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Cross-Section Bootstrap: Unveiling the Froissart Amplitude
A universal finite-energy upper bound on the integrated cross-section for identical scalars is derived; the conjectured saturating "Froissart amplitude" shows Regge trajectories, a rising cross-section, and annulus-li...
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Bounds on the next-to-leading Wilson coefficient in maximal supergravity
The next-to-leading Wilson coefficient in D=7 maximal supergravity is minimized at the same U-duality symmetric point as the leading coefficient, supporting string universality.
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Analytic bootstrap bounds on masses and spins in gravitational and non-gravitational scalar theories
The authors derive 'Sequential Spin and Mass Constraints' for su-symmetric and stu-symmetric four-point amplitudes, claiming any weakly-coupled spectrum must have ordered spins and bounded mass ratios.
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