In large N conformal field theories, states built from light scalar operators or stress tensors can have negative smeared null energy, but the negative amount is bounded by a scale set by the central charge.
A New Spin on Causality Constraints
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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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How negative can null energy be in large N CFTs?
In large N conformal field theories, states built from light scalar operators or stress tensors can have negative smeared null energy, but the negative amount is bounded by a scale set by the central charge.