On the computable cross norm in tensor networks and holography - Alexey Milekhin; Pratik Rath; Wayne Weng (Journal of High Energy Physics)
Abstract The computable cross norm or realignment (CCNR) was recently discussed in ref. [1] as a measure of multipartite entanglement in a condensed matter context. In this short note, we point out that it is closely related to the (2, n)-Rényi reflected entropy, which has been studied in the context of AdS/CFT. We discuss the calculation of the CCNR in random tensor networks as well as holographic CFTs. The holographic dual involves a backreacted entanglement wedge cross section in a geometry sourced by Rényi-2 cosmic branes. We perform explicit calculations for two intervals in a hyperbolic random tensor network as well the vacuum state of a 2D holographic CFT, and analyze the occurence of a connected-to-disconnected phase transition. The example illustrates the validity of the proposal for analytic continuation in holography for arbitrary values of Rényi parameter n. We comment on a symmetry-resolved generalization of this quantity.