Abstract
Causality in a shockwave state is related to the analytic properties of a
four-point correlation function. Extending recent results for scalar probes, we
show that this constrains the couplings of the stress tensor to light spinning
operators in conformal field theory, and interpret these constraints in terms
of the interaction with null energy. For spin-1 and spin-2 conserved currents
in four dimensions, the resulting inequalities are a subset of the
Hofman-Maldacena conditions for positive energy deposition. It is well known
that energy conditions in holographic theories are related to causality on the
gravity side; our results make a connection on the CFT side, and extend it to
non-holographic theories.
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