In this paper we define a natural generalization of the von Neumann entropy to multiple parties that is symmetric with respect to all the parties. We call this measure multi-entropy. We show that for conformal field theories with holographic duals, the multi-entropy is computed by the area of an appropriate “soap-film” anchored on the boundary. We conjecture the quantum version of this prescription that takes into account the subleading corrections in $G_N$.

• Received 30 August 2022
• Accepted 24 October 2022

DOI:https://doi.org/10.1103/PhysRevD.106.126001

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Published by the American Physical Society