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.
Quantum Energy Inequality for the Massive Ising Model
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abstract
A Quantum Energy Inequality (QEI) is derived for the massive Ising model, giving a state-independent lower bound on suitable averages of the energy density; the first QEI to be established for an interacting quantum field theory with nontrivial S-matrix. It is shown that the Ising model has one-particle states with locally negative energy densities, and that the energy density operator is not additive with respect to combination of one-particle states into multi-particle configurations.
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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.