Surface/State Correspondence as a Generalized Holography

By Masamichi Miyaji, T. Takayanagi. 2015

198 citations recorded by the source corpus.

We propose a new duality relation between codimension two space-like surfaces in gravitational theories and quantum states in dual Hilbert spaces. This surface/state correspondence largely generalizes the idea of holography such that we do not need to rely on any existence of boundaries in gravitational spacetimes. The present idea is motivated by the recent interpretation of AdS/CFT in terms of the tensor networks so called MERA. Moreover, we study this correspondence from the viewpoint of entanglement entropy and information metric. The Cramer-Rao bound in quantum estimation theory implies that the quantum fluctuations of radial coordinate of the AdS is highly suppressed in the large N limit.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a6eb1dc604432f460f5c4ab679e18f608ff2f607

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. R. Myers
2. T. Takayanagi
3. Ro Jefferson
4. Paweł Caputa
5. Masamichi Miyaji
6. Kento Watanabe
7. N. Kundu
8. Koji Umemoto

In Nuclear and High Energy Physics

1. R. Myers
2. T. Takayanagi
3. Ro Jefferson
4. Masamichi Miyaji
5. Paweł Caputa
6. Koji Umemoto
7. Kento Watanabe
8. N. Kundu

In Statistical and Nonlinear Physics

1. R. Myers
2. T. Takayanagi
3. Ro Jefferson
4. Masamichi Miyaji
5. Koji Umemoto
6. Paweł Caputa
7. Kento Watanabe
8. N. Kundu

Citations in the corpus

• Entanglement of purification through holographic duality (2017, background): “In a gravity background with a tensor network description, we can define a pure state for any codimension two convex surface, called surface/state correspondence [6].”
• Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT (2017, background): “There already exists a formulation called cMERA (continuous MERA) [4], whose connection to AdS/CFT has been explored in [6, 7, 10, 12, 16].”
• Circuit complexity in quantum field theory (2017, background): “At present, it is actually not clear how the reference state enters in the holographic calculations at all, but perhaps one can draw upon the proposal for a statesurface conjecture in [58].”