The Momentum Kernel of Gauge and Gravity Theories

TL;DR

This paper introduces a momentum kernel that factorizes string amplitudes into open string amplitudes, connects to field theory limits, and reveals new relations and links between gravity and gauge theories.

Contribution

It provides an explicit formula for the momentum kernel, unifying string and field theory amplitude relations and exploring gravity-gauge theory connections.

Findings

Derived explicit formula for the momentum kernel.

Connected the kernel to monodromy relations and minimal amplitude basis.

Explored implications for soft limits and gravity-gauge links.

Abstract

We derive an explicit formula for factorizing an $n$-point closed string amplitude into open string amplitudes. Our results are phrased in terms of a momentum kernel which in the limit of infinite string tension reduces to the corresponding field theory kernel. The same momentum kernel encodes the monodromy relations which lead to the minimal basis of color-ordered amplitudes in Yang-Mills theory. There are interesting consequences of the momentum kernel pertaining to soft limits of amplitudes. We also comment on surprising links between gravity and certain combinations of kinematic and color factors in gauge theory.