Proof of Renyi QNEC for free fermions

Abstract: Quantum null energy condition (QNEC) is usually stated as a bound on the expectation value of null components of the stress energy tensor at a point in terms of second null shape variations of the entanglement entropy at the same point. It can be recast as the statement that the sign of the second null shape variation of the relative entropy of any state with respect to the vacuum is positive. Using instead a Renyi generalization of relative entropy, called sandwiched Renyi divergence (SRD), leads to what is termed the Renyi QNEC: the second null shape variation of SRD of any state with respect to the vacuum is positive. In this work, we prove the Renyi QNEC for free and superrenormalizable fermionic quantum field theories in spacetime dimensions greater than 2 using null quantization, for the case where the Renyi parameter $n>1$. We end with comments on multiple possible generalizations.