Abstract
A new principle in quantum gravity, dubbed spacetime complexity, states that gravitational physics emerges from spacetime seeking to optimize the computational cost of its quantum dynamics. Thus far, this principle has been realized at the linearized level, in holographic theories with Einstein gravity duals, assuming the so-called ‘Complexity-Volume’ (CV) proposal. We expand on this proof in two significant directions. First, we derive higher-derivative gravitational equations by including appropriate corrections to the CV dictionary. Second, we show semi-classical equations arise by considering the leading bulk quantum corrections to CV. Our proof is valid for two-dimensional dilaton gravities, where the problem of semi-classical backreaction can be solved exactly. However, we argue the principle should hold more generally, leading us to a concrete proposal for bulk complexity of perturbative excited states in arbitrary dimensions. Our results demonstrate the robustness of spacetime complexity as a guiding principle to understand gravity in terms of quantum computation.
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Acknowledgments
We are grateful to José Barbón, Elena Cáceres, César Gómez, Michal Heller, Juan Hernandez, Nima Lashkari, Bahman Najian, Ayan Patra, Andrew Rolph, Brian Swingle, Jeremy van der Heijden, and Claire Zukowski for useful discussions and comments on the manuscript. RC and JFP are supported by the ‘Atracción de Talento’ program grant 2020-T1/TIC-20495 and by the Spanish Research Agency via grants CEX2020-001007-S and PID2021-123017NB-I00, funded by MCIN/AEI/10.13039/501100011033 and by ERDF A way of making Europe. AS is supported by the Simons Foundation via the It from Qubit Collaboration and by EPSRC. AS and ZWD acknowledge IFT-Madrid for hospitality while this work was being completed.
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Carrasco, R., Pedraza, J.F., Svesko, A. et al. Gravitation from optimized computation: Einstein and beyond. J. High Energ. Phys. 2023, 167 (2023). https://doi.org/10.1007/JHEP09(2023)167
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DOI: https://doi.org/10.1007/JHEP09(2023)167