Bootstrap Principle for the Spectrum and Scattering of Strings
Clifford Cheung, Aaron Hillman, Grant N. Remmen
Abstract
We show that the Veneziano amplitude of string theory is the unique solution to an analytically solvable bootstrap problem. Uniqueness follows from two assumptions: faster than power-law falloff in high-energy scattering and the existence of some infinite sequence in momentum transfer at which higher-spin exchanges cancel. The string amplitude-including the mass spectrum-is an output of this bootstrap. If the amplitude merely vanishes at high energies, the solution is a three-parameter family containing the Veneziano, Coon, and hypergeometric amplitudes, and more.
Topics & Concepts
PhysicsScattering amplitudeAmplitudeHypergeometric functionUniquenessSpectrum (functional analysis)String (physics)String theoryMomentum (technical analysis)Quantum electrodynamicsMomentum transferMathematical physicsScatteringQuantum mechanicsSpin (aerodynamics)Mathematical analysisMathematicsEconomicsThermodynamicsFinanceParticle physics theoretical and experimental studiesBlack Holes and Theoretical PhysicsQuantum Chromodynamics and Particle Interactions