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Uniqueness Criteria for the Virasoro-Shapiro Amplitude
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The scattering amplitudes of string theory exhibit many extraordinary properties. But are they the unique mathematical objects to do so? Recently, it has been shown how the spectrum and amplitudes of open string theory follow directly from the assumptions of faster than power-law falloff at high energies and a property dubbed level truncation. At present there is no analogous principle for closed string scattering, which is famously rigid and naively impervious to modification. In this paper we analytically bootstrap the spectrum and four-point amplitudes of the closed string -- together with a parameterized space of deformations -- from conditions on high-energy falloff and level truncation. While these deformations exhibit the same Regge scaling as pure gravity, in the tensionless limit they reproduce remarkable extremal amplitudes that have appeared in bottom-up studies of positivity.
Forward citations
Cited by 19 Pith papers
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String Theory from Maximal Supersymmetry
The open string Veneziano amplitude emerges as the unique tree-level completion of N=4 super Yang-Mills when supersymmetry, factorization, and positivity are imposed.
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Analytic Boundaries of Infinite-Spin-Tower Amplitudes from Hidden Zero
The exact analytic boundary of unitary infinite-spin-tower amplitudes is derived and shown to be maximal unless energy poles accumulate.
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Gravitational Effective Theories with Maximal Supersymmetry and a Peculiar Parity
Peculiar parity plus N=8 SUSY, tree-level factorization, and finitely many states at the mass gap uniquely select the Virasoro–Shapiro amplitude among weakly-coupled UV completions of N=8 supergravity.
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Bootstrapping black holes at low impact parameter
After subtracting the eikonal carrier, the residual SDR spectrum in six dimensions organizes into a cap-saturated low-impact band, an empty gap, and Regge-like ridges whose weak-coupling edge is the G_N=0 baseline.
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Bootstrapping black holes at low impact parameter
After eikonal subtraction, finite-grid SDR bootstrap extremal spectra support a cap-saturated black-hole-scale band and Regge-like ridge while leaving the intervening gap mostly empty.
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Meromorphic amplitudes from 3-dimensional supersymmetry
Coon amplitude equals 3d N=2 half-index of XYZ model with boundary conditions; IR flow gives Veneziano amplitude, and elliptic completion of q^ST yields a meromorphic positive version.
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Analytic Bootstrap of the Veneziano Amplitude
The Veneziano amplitude is the unique solution to a dual bootstrap from dispersive sum rules interpreted as moments, unitarity, and string monodromy or splitting conditions.
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Analytic Bootstrap of the Veneziano Amplitude
The Veneziano amplitude is the unique outcome of an analytic dual bootstrap from dispersive sum rules, unitarity, and either string monodromy or splitting and hidden-zero conditions.
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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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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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Uniqueness and Analytic Structures of Bosonic String Effective Amplitudes
Gauge invariance, locality, and cyclicity uniquely fix dimension-raising operators for zero-transcendentality bosonic string amplitudes, yielding recursive construction from Yang-Mills and factorization via inverse op...
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A Dispersive Bootstrap for the Virasoro-Shapiro Amplitude
Dispersive bootstrap with unitarity, crossing and a Virasoro-inspired ansatz isolates the Virasoro-Shapiro amplitude in a small island for the gravity-pole-subtracted four-point amplitude in 10D supersymmetry.
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Multipositivity Constrains the Chiral Lagrangian
Multipositivity bounds derived from planar tree-level scattering amplitudes constrain Wilson coefficients of the chiral Lagrangian from below by the chiral anomaly.
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The Equivalence Principle at High Energies Completes the Spectrum
Tree-level gravitational scattering under the equivalence principle mandates single-particle states in all irreducible representations constructible from a single seed charge, with equal interaction strengths.
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Sampling the Graviton Pole and Deprojecting the Swampland
A sampling-based bootstrap for graviton poles in EFTs yields non-projective bounds that fix the EFT cutoff scale relative to the Planck mass, with M/M_P ≲ 7.8 in D=5.
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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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Completeness from Gravitational Scattering
Symmetry plus perturbative gravitational scattering consistency requires the abelian charge lattice to be completely populated by single-particle states for SU(N) with N≥3 and SO(N) with N≥5.
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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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