Abstract
We propose a new formula for computing holographic Renyi entropies in the presence of multiple extremal surfaces. Our proposal is based on computing the wave function in the basis of fixed-area states and assuming a diagonal approximation for the Renyi entropy. For Renyi index n ≥ 1, our proposal agrees with the existing cosmic brane proposal for holographic Renyi entropy. For n < 1, however, our proposal predicts a new phase with leading order (in Newton’s constant G) corrections to the cosmic brane proposal, even far from entanglement phase transitions and when bulk quantum corrections are unimportant. Recast in terms of optimization over fixed-area states, the difference between the two proposals can be understood to come from the order of optimization: for n < 1, the cosmic brane proposal is a minimax prescription whereas our proposal is a maximin prescription. We demonstrate the presence of such leading order corrections using illustrative examples. In particular, our proposal reproduces existing results in the literature for the PSSY model and high-energy eigenstates, providing a universal explanation for previously found leading order corrections to the n < 1 Renyi entropies.
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Acknowledgments
We are very grateful to Geoff Penington for extremely helpful discussions. XD is 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. JKF is supported by the Marvin L. Goldberger Member Fund at the Institute for Advanced Study and the National Science Foundation under Grant No. PHY-2207584. PR is supported in part by a grant from the Simons Foundation, by funds from UCSB, the Berkeley Center for Theoretical Physics; by the Department of Energy, Office of Science, Office of High Energy Physics under QuantISED Award DE-SC0019380, under contract DE-AC02-05CH11231 and by the National Science Foundation under Award Number 2112880. This material is based upon work supported by the Air Force Office of Scientific Research under award number FA9550-19-1-0360.
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Dong, X., Kudler-Flam, J. & Rath, P. A modified cosmic brane proposal for holographic Renyi entropy. J. High Energ. Phys. 2024, 120 (2024). https://doi.org/10.1007/JHEP06(2024)120
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DOI: https://doi.org/10.1007/JHEP06(2024)120