|
Abstract |
The four-dimensional $S$-matrix will be reconsidered as a correlator on the celestial sphere
at null infinity. Asymptotic particle states can be characterized by the point at which they
enter or exit the celestial sphere as well as their $SL(2,\mathbb C)$ Lorentz quantum
numbers: namely their conformal scaling dimension and spin $h\pm \bar h$ instead of the
energy and momentum. This characterization precludes the notion of a soft particle whose
energy is taken to zero which plays an important role in the conventional formulation of
quantum field theory scattering amplitudes. We propose that in this new formulation it should
be replaced by the notion of a {\it conformally soft} particle with $h=0$ or $\bar h=0$. For
photons and gravitons we explicitly construct conformally soft $SL(2,\mathbb C)$ currents
with dimensions $(1,0)$ and $(2,0)$ respectively and identify them with the generators of a
$U(1)$ Kac-Moody symmetry on the celestial sphere and celestial conformal symmetry. BMS
supertranslations are generated by a spin-one current whose OPE relation looks quite unusual
from the celestial CFT$_2$ perspective but is equivalent to the leading soft graviton theorem
and may usefully constrain celestial correlators in quantum gravity. |
