Description
Abstract: Scattering amplitudes play a prominent role not only in high
energy particle physics, but also for quantum gravity in
asymptotically flat spacetime.The search for a "theory at infinity” of
the S-Matrix has revealed surprising geometric structures underlying
amplitudes ranging from the string worldsheet to the amplituhedron,
but these are all geometries in auxiliary spaces as opposed to the
space at infinity where amplitudes actually live. By thinking of
amplitudes as differential forms, we propose a novel geometric picture
directly in kinematic space for a wide range of massless theories in
general dimensions.
As a primary example, we show that tree amplitudes of bi-adjoint
scalars are given by the “volume” of an associahedron living naturally
in kinematic space, and scattering equations act as a diffeomorphism
from the open-string moduli space (also an associahedron) to it. We
find general “scattering forms” dual to color-dressed amplitudes e.g.
for gluons and pions, which is possible due to a remarkable fact --
“Color is Kinematics”. All these forms are well-defined in
projectivized space, a property which provide a geometric origin for
color-kinematics duality.
