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PIRSA:15020134

Exact holographic mapping, tensor networks and space-time geometry

APA

Qi, X. (2015). Exact holographic mapping, tensor networks and space-time geometry. Perimeter Institute for Theoretical Physics. https://pirsa.org/15020134

Xiaoliang Qi Stanford University

Talk numberPIRSA:15020134
Source RepositoryPIRSA
Collection

Abstract

Holographic duality is a duality between gravitational systems and non-gravitational systems. In this talk, I will propose a different approach for understanding holographic duality named as the exact holographic mapping. The key idea of this approach can be summarized by two points: 1) The bulk theory and boundary theory are related by a unitary mapping in the Hilbert space. 2) Space-time geometry is determined by the structure of correlations and quantum entanglement in a quantum state. When applied to lattice systems, the holographic mapping is defined by a unitary tensor network. For free fermion boundary theories, I will discuss how different bulk geometries are obtained as dual theories of different boundary states. A particularly interesting case is the AdS black hole geometry and the interpretation of the interior of a black hole. We will also discuss dual geometries of topological states of matter.