New multipartite entanglement measure and its holographic dual

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 GN.