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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 1: Quantum Information and Complexity

MP 1.1: Hauptvortrag

Montag, 19. März 2018, 16:00–16:45, Z6 - SR 1.012

Quantum Information and Topological Complexity in AdS/CFT — •René Meyer¹, Raimond Abt¹, Johanna Erdmenger¹, Haye Hinrichsen¹, Charles M. Melby-Thompson¹, Christian Northe¹, and Ignacio A. Reyes^1,2 — ¹Institut für Theoretische Physik und Astrophysik, Julius-Maximilians-Universität Würzburg, Am Hubland, 97074 Würzburg — ²Instituto de Fisica, Pontificia Universidad Catolica de Chile, Casilla 306, Santiago, Chile

Recently, using the AdS/CFT correspondence exciting new relations are being established between aspects of quantum information theory and of the geometry of black holes in Anti de Sitter space-times. After a concise review of the roles of entanglement measures such as e.g. the entanglement entropy as well as of the computational complexity within the AdS/CFT correspondence, I discuss the notion of subregion complexity of a 2D critical state from three different viewpoints: the AdS3/CFT2 correspondence, random tensor networks, and kinematic space. From the AdS3/CFT2 point of view I explain how in the discontinuity of subregion complexity as given by the volume within the Ryu-Takayanagi surface is related to the Euler characteristic of the respective bulk regions via the Gauss-Bonnet theorem. I then discuss how the volume of these sub regions can be calculated in kinematic space, which is the space of geodesics on the time-slice of AdS3, and present a new CFT expression of subregion complexity. Finally, I present results that qualitatively reproduce the discontinuity in complexity in a tensor network approach. Based on arXiv:1710.01327 [hep-th].