Events Calendar
Beyond Toy Models: Distilling Tensor Networks in Full AdS/CFT
Thursday March 28, 2019
3:30 pm
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Presenter:  Ning Bao, UC Berkeley 

Series:  CQuIC Seminars  
Abstract: 
We present a general procedure for constructing tensor networks that accurately reproduce holographic states in conformal field theories (CFTs). Given a state in a largeN CFT with a static, semiclassical gravitational dual, we build a tensor network by an iterative series of approximations that eliminate redundant degrees of freedom and minimize the bond dimensions of the resulting network. We argue that the bond dimensions of the tensor network will match the areas of the corresponding bulk surfaces. For 'tree' tensor networks (i.e., those that are constructed by discretizing spacetime with nonintersecting RyuTakayanagi surfaces), our arguments can be made rigorous using a version of oneshot entanglement distillation in the CFT. Using the known quantum error correcting properties of AdS/CFT, we show that bulk legs can be added to the tensor networks to create holographic quantum error correcting codes. These codes behave similarly to previous holographic tensor network toy models, but describe actual bulk excitations in continuum AdS/CFT.
By assuming some natural generalizations of the 'holographic entanglement of purification' conjecture, we are able to construct tensor networks for more general bulk discretizations, leading to finergrained networks that partition the information content of a RyuTakayanagi surface into tensorfactorized subregions. While the granularity of such a tensor network must be set larger than the string/Planck scales, we expect that it can be chosen to lie well below the AdS scale. However, we also prove a nogo theorem which shows that the bulktoboundary maps cannot all be isometries in a tensor network with intersecting RyuTakayanagi surfaces. 

Host:  Elizabeth Crosson  
Location:  Room 190, Physics & Astronomy  