Amplitudes Summer School 2017: Chia-Hsien Shen - Unifying Relations for Scattering Amplitudes
From Einan Gardi
Unifying Relations for Scattering Amplitudes
Abstract: The talk is based on 1612.00868 and work to appear with Clifford Cheung and Congkao Wen. We derive new scattering amplitudes relations which reveal a hidden unity among theories of diverse spins in general spacetime dimensions. These relations are built from a set of Lorentz invariant differential operators which transmute states of higher spin into states of lower spin. Transmutation takes amplitudes of gravity coupled to a dilaton and two-form into any amplitude in Einstein- Yang-Mills, the special Galileon, and (Dirac-)Born-field theory. Starting from Yang-Mills amplitudes, the transmutation covers any amplitude in gauged bi-adjoint scalar theory and the non-linear sigma model. As a corollary, known properties of gauge theory and gravity amplitudes like the Weinberg soft theorems, color-kinematics duality, the KLT relations, and the CHY construction are trivially inherited by the transmuted amplitudes. In the case of the non-linear sigma model, the recently found kinematic algebra becomes obvious from this construction.