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- W3100251214 abstract "The quantum null energy condition (QNEC) is a conjectured bound on components $(T_{kk} = T_{ab} k^a k^b$) of the stress tensor along a null vector $k^a$ at a point $p$ in terms of a second $k$-derivative of the von Neumann entropy $S$ on one side of a null congruence $N$ through $p$ generated by $k^a$. The conjecture has been established for super-renormalizeable field theories at points $p$ that lie on a bifurcate Killing horizon with null tangent $k^a$ and for large-N holographic theories on flat space. While the Koeller-Leichenauer holographic argument clearly yields an inequality for general $(p,k^a)$, more conditions are generally required for this inequality to be a useful QNEC. For $dle 3$, for arbitrary backgroud metric satisfying the null convergence condition $R_{ab} k^a k^b ge 0$, we show that the QNEC is naturally finite and independent of renormalization scheme when the expansion $theta$ and shear $sigma_{ab}$ of $N$ at point $p$ satisfy $theta |_p= dot{theta}|_p =0$, $sigma_{ab}|_p=0$. This is consistent with the original QNEC conjecture. But for $d=4,5$ more conditions are required. In particular, we also require the vanishing of additional derivatives and a dominant energy condition. In the above cases the holographic argument does indeed yield a finite QNEC, though for $dge6$ we argue these properties to fail even for weakly isolated horizons (where all derivatives of $theta, sigma_{ab}$ vanish) that also satisfy a dominant energy condition. On the positive side, a corrollary to our work is that, when coupled to Einstein-Hilbert gravity, $d le 3$ holographic theories at large $N$ satisfy the generalized second law (GSL) of thermodynamics at leading order in Newton's constant $G$. This is the first GSL proof which does not require the quantum fields to be perturbations to a Killing horizon." @default.
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- W3100251214 date "2017-10-31" @default.
- W3100251214 modified "2023-09-27" @default.
- W3100251214 title "The quantum null energy condition in curved space" @default.
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- W3100251214 doi "https://doi.org/10.1088/1361-6382/aa8f2c" @default.
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