On the quantum Bousso bound in JT gravity

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 \(2\pi {k}^{\mu }{k}^{\nu }\langle :{T}_{\mu \nu }:\rangle -{S}^{{\prime}{\prime}}-\frac{6}{c}{\left({S}{\prime}\right)}^{2}\) 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.