Abstract
We transform superstring scattering amplitudes into the correlation functions of primary conformal fields on two-dimensional celestial sphere. The points on celestial sphere are associated to the asymptotic directions of (light-like) momenta of external particles, with the Lorentz group realized as the SL(2,C) conformal symmetry of the sphere. The energies are dualized through Mellin transforms into the parameters that determine dimensions of the primaries. We focus on four-point amplitudes involving gauge bosons and gravitons in type I open superstring theory and in closed heterotic superstring theory at the tree-level.
Highlights
In modern-day particle colliders, accelerators produce beams of incident particles with specific energies and momenta, described to a reasonable accuracy by the packets of plane waves with a narrow spread of four-momentum
Which are Mellin transforms of the usual plane waves. These packets are described by massless scalar conformal primary wave functions of dimension ∆, the variable dual to the energy in the Mellin sense, and can be generalized to higher spin [7]. By using such Mellin transforms, “old-fashioned” gauge and gravitational amplitudes can be converted into conformal correlators of primary fields on celestial sphere, labeled by their conformal spin and dimensions
The Lorentz group is realized as the conformal symmetry of the sphere
Summary
In modern-day particle colliders, accelerators produce beams of incident particles with specific energies and momenta, described to a reasonable accuracy by the packets of plane waves with a narrow spread of four-momentum. Which are Mellin transforms of the usual plane waves These packets are described by massless scalar conformal primary wave functions of dimension ∆, the variable dual to the energy in the Mellin sense, and can be generalized to higher spin [7]. By using such Mellin transforms, “old-fashioned” gauge and gravitational amplitudes can be converted into conformal correlators of primary fields on celestial sphere, labeled by their conformal spin and dimensions. As we will see later, this uncontrollable growth at large energies poses an obstacle for transforming gravitational amplitudes to celestial sphere This problem does not appear in string amplitudes which are renowned for their super-soft ultraviolet behavior [16,17]. We will start from the amplitudes with three external particles, for which there is no difference between QFT and string theory
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