On the Quantum Bousso Bound in JT gravity

Abstract

We prove the Strominger-Thompson quantum Bousso bound in the infinite class of conformal vacua in semiclassical JT gravity, with postive or negative cosmological constant. The Bousso-Fisher-Leichenauer-Wall quantum Bousso bound follows from an analogous derivation, requiring only initial quantum non-expansion. In this process, we show that the quantity $2\pi k^{\mu }{k}^{\nu }<:T_{\mu \nu }:>-S^{\prime \prime }-\frac{6}{c}(S^{\prime }{)}^2$ vanishes in any vacuum state, entailing a stronger version of Wall's quantum null energy condition. We derive an entropy formula in the presence of a generic class of two reflecting boundaries, in order to apply our argument to the half reduction model of de Sitter JT gravity.

46 pages, 5 figures. Published version