Scattering Equations and String Theory Amplitudes

TL;DR

The paper builds a bridge between the CHY scattering-equations framework and string theory by proposing a dual model whose amplitudes are localized on the scattering-equation surface. This model reproduces field-theory results in the $\alpha'\to0$ limit while capturing Gross-Mende-type behavior for large $\alpha'$, and it extends naturally to gauge fields, fermions, and mixed states through a delta-function measure enforcing the scattering equations. A key technical device is the decomposition of open-string integrands into Pfaffians plus $1/\alpha'$ corrections that disappear on the scattering-equation surface via integration by parts, allowing exact CHY-like results to emerge. The authors provide explicit checks for four-fermion, two-fermion-two-gluon, and five-point mixed amplitudes, demonstrating agreement with known results and suggesting a robust, computable framework for tree-level amplitudes across particle types. This work deepens the connection between CHY/ambitwistor approaches and string theory, with potential implications for closed-string and loop extensions.

Abstract

Scattering equations for tree-level amplitudes are viewed in the context of string theory. As a result of the comparison we are led to define a new dual model which coincides with string theory in both the small and large $α'$ limit, and whose solution is found algebraically on the surface of solutions to the scattering equations. Because it has support only on the scattering equations, it can be solved exactly, yielding a simple resummed model for $α'$-corrections to all orders. We use the same idea to generalize scattering equations to amplitudes with fermions and any mixture of scalars, gluons and fermions. In all cases checked we find exact agreement with known results.