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