Abstract
In this paper, we systematically study the measures of multi-partite entanglement with the aim of constructing those measures that can be computed in probe approximation in the holographic dual. We classify and count general measures as invariants of local unitary transformations. After formulating these measures in terms of permutation group elements, we derive conditions that a probe measure should satisfy and find a large class of solutions. These solutions are generalizations of the multi-entropy introduced in [1]. We derive their holographic dual with the assumption that the replica symmetry is unbroken in the bulk and check our prescription with explicit computations in 2d CFTs. Analogous to the multi-entropy, the holographic dual of these measures is given by the weighted area of the minimal brane-web but with branes having differing tensions. We discuss the replica symmetry assumption and also how the already known entanglement measures, such as entanglement negativity and reflected entropy fit in our framework.
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Acknowledgments
We would like to thank Xi Dong, Jonathan Harper, Matthew Headrick, Gautam Mandal, Shiraz Minwalla, Arvind Nair, Pratik Rath, Pranab Sen, Piyush Shrivastava, Douglas Stanford, Sandip Trivedi for interesting discussions. We are particularly indebted to Onkar Parrikar for stimulating discussions and insightful comments. We would also like to thank Shraiyance Jain and Harshal Kulkarni for their collaboration on related projects. This work is supported by the Infosys Endowment for the study of the Quantum Structure of Spacetime and by the SERB Ramanujan fellowship. We acknowledge the support of the Department of Atomic Energy, Government of India, under Project Identification No. RTI 4002. AG would like to thank the hospitality of KITP during the program “Bootstrapping quantum gravity” where this work was partially carried out. Finally, we acknowledge our debt to the people of India for their steady support to the study of the basic sciences.
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Gadde, A., Krishna, V. & Sharma, T. Towards a classification of holographic multi-partite entanglement measures. J. High Energ. Phys. 2023, 202 (2023). https://doi.org/10.1007/JHEP08(2023)202
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DOI: https://doi.org/10.1007/JHEP08(2023)202