Null states and time evolution in a toy model of black hole dynamics

TL;DR

This paper explores how non-perturbative effects influence the time evolution of a simplified gravity model, revealing significant deviations from perturbative predictions even when the number of operators is small.

Contribution

It demonstrates that non-perturbative effects can significantly alter dynamics in a toy gravity model without quantum extremal surfaces, especially for small operator insertions.

Findings

Non-perturbative effects impact time evolution even for N ≪ e^S.

Discrepancies between non-perturbative and perturbative evolution are small when operators act on a small subspace.

The study provides insights into potential effects in more realistic gravitational systems.

Abstract

Spacetime wormholes can provide non-perturbative contributions to the gravitational path integral that make the actual number of states $e^S$ in a gravitational system much smaller than the number of states $e^{S_{\mathrm{p}}}$ predicted by perturbative semiclassical effective field theory. The effects on the physics of the system are naturally profound in contexts in which the perturbative description actively involves $N = O(e^S)$ of the possible $e^{S_{\mathrm{p}}}$ perturbative states; e.g., in late stages of black hole evaporation. Such contexts are typically associated with the existence of non-trivial quantum extremal surfaces. However, by forcing a simple topological gravity model to evolve in time, we find that such effects can also have large impact for $N\ll e^S$ (in which case no quantum extremal surfaces can arise). In particular, even for small $N$, the insertion of generic operators into the path integral can cause the non-perturbative time evolution to differ dramatically from perturbative expectations. On the other hand, this discrepancy is small for the special case where the inserted operators are non-trivial only in a subspace of dimension $D \ll e^S$. We thus study this latter case in detail. We also discuss potential implications for more realistic gravitational systems.