Modular Fluctuations from Shockwave Geometries

Abstract

Modular fluctuations have previously been shown to obey an area law $⟨\Delta K^2⟩=⟨K⟩=A/4G_N$. 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.

22 pages, 4 figures

References in corpus (1)

• Snowmass 2021 White Paper: Observational Signatures of Quantum Gravity