On Entanglement Entropy And Quantum Complexity In Qft And Holography

On Entanglement Entropy and Quantum Complexity in QFT and Holography

Discrete Holography: Through the Quantum Information Looking-Glass

How can we reconcile general relativity with quantum mechanics? One promising approach is the holographic principle, which posits that quantum gravity can be described by a lower-dimensional theory without gravity. This book advances the field of discrete holography by building models on discretizations of hyperbolic space, extending the AdS/CFT correspondence and enabling experimental tests of holographic predictions. The first part develops discrete bulk models on hyperbolic tilings, exploring scalar field instability and correlation functions, and proposes electric circuits as experimental platforms. The second part constructs boundary theories as disordered spin chains and analyzes their entanglement via tensor networks. The final part investigates quantum information measures—circuit complexity, geometric quantum discord, and operator algebras—to probe black hole properties in holographic dualities. This work uncovers new insights into holography and bridges theoretical concepts with experimental realizations.

AdS3/CFT2 and Holographic Entanglement Entropy

This book focuses on AdS3/CFT2, addressing different aspects of this correspondence in field theory and in gravity, including entanglement entropy, higher genus partition function, and conformal block. Holographic entanglement entropy is an important area in holographic and quantum information, which implies a deep relation between geometry and quantum entanglement. In this book, the authors use holographic entanglement entropy as a tool to investigate AdS3/CFT2. They study the entanglement entropy at high temperature in field theory and in holographics, and show that the results match each other in classical and one-loop order. In the AdS3/CFT2 system, they examine in detail the correspondence, exploring the higher genus partition function, entanglement entropy in a general system and conformal block, and they find good correspondence in field theory and gravity. The result strongly supports AdS3/CFT2 correspondence. In addition, they develop several important techniques in 2d CFT and 3d gravity, which also offer inspiration for other fields.