Modular fluctuations from shockwave geometries

Abstract

Modular fluctuations have previously been shown to obey an area law $⟨\mathrm{\ensuremath{\Delta}}{K}^{2}⟩=⟨K⟩=A/4{G}_{N}$. Furthermore, modular fluctuations generate fluctuations in the spacetime geometry of empty causal diamonds. Here we demonstrate the physical origin of these fluctuations, showing that the modular area law, in $d$-dimensionsal Minkowski space, can be reproduced from shockwaves arising from vacuum fluctuations. The size of the vacuum fluctuations is fixed by commutation relations in light-ray operators, of the same form postulated by 't Hooft in the context of black hole horizons.

Topics & Concepts