Quantum Null Energy Condition in the holographic dual of Gauss-Bonnet gravity

Abstract

The Quantum Null Energy Condition (QNEC) is the extension of the classical Null Energy Condition (NEC) into the quantum physics regime. This new energy condition relates the classical NEC to the second derivative of an entanglement entropy in the corresponding null direction k. In this thesis, we perform an explicit computation of the QNEC for two different geometries of the entangling region in which we compute the entanglement entropy, namely strip-like and spherical regions, and we do so by considering both Einstein-Hilbert and Gauss-Bonnet holographies. We show that, in Einstein-Hilbert holography, for the strip-like regions the QNEC is always trivially satisfied while for spheres we can encounter a saturation of the inequality depending on how we choose the null direction k. This saturation will not show up in the Gauss-Bonnet holography setup and, instead, we will find that the QNEC is violated depending on the sign of the Gauss-Bonnet coupling. Therefore, these results may add more arguments to the already existing discussion on whether the field theory dual to Gauss-Bonnet gravity is actually physical or not.