Abstract
Spacetime wormholes can provide non-perturbative contributions to the gravitational path integral that make the actual number of states eS in a gravitational system much smaller than the number of states \( {e}^{S_{\textrm{p}}} \) 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(eS) of the possible \( {e}^{S_{\textrm{p}}} \) 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 ≪ eS (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 ≪ eS. We thus study this latter case in detail. We also discuss potential implications for more realistic gravitational systems.
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Acknowledgments
The authors thank Geoff Penington for discussions of non-isometric codes. The work of XD was supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011702, and by funds from the University of California. The work of MK, XL, DM, and ZW was supported by NSF grant PHY-2107939 and by funds from the University of California. ZW was also supported by Air Force Office of Scientific Research under award number FA9550-19-1-036 and by the DOE award number DE-SC0015655. This research was supported in part by grant NSF PHY-2309135 to the Kavli Institute for Theoretical Physics (KITP).
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Dong, X., Kolanowski, M., Liu, X. et al. Null states and time evolution in a toy model of black hole dynamics. J. High Energ. Phys. 2024, 199 (2024). https://doi.org/10.1007/JHEP08(2024)199
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DOI: https://doi.org/10.1007/JHEP08(2024)199