Discussion of Entanglement Entropy in Quantum Gravity

• Published in: Fortschritte der Physik Vol. 66; no. 2
• Main Author: Ma, Chen‐Te
• Format: Journal Article
• Language: English
• Published: Weinheim Wiley Subscription Services, Inc 01.02.2018
• Subjects: conformal field theory; Entropy; Field theory; Magnetic fields; models of quantum gravity; Quantum entanglement; Quantum gravity; Quantum theory; topological field theories; Two dimensional analysis; Two dimensional models
• ISSN: 0015-8208; 1521-3978
• DOI: 10.1002/prop.201700095

We study entanglement entropy in gravity theory with quantum effects. A simplest model is a two dimensional Einstein gravity theory. We use an n‐sheet manifold to obtain an area term of entanglement entropy by summing over all background fields. Based on AdS/CFT correspondence, strongly coupled conformal field theory is expected to describe perturbative quantum gravity theory. An ultraviolet complete quantum gravity theory should not depend on a choice of an entangling surface. To analysis the problem explicitly, we analyze two dimensional conformal field theory. We find that a coefficient of a universal term of entanglement entropy is independent of a choice of an entangling surface in two dimensional conformal field theory for one interval to show a tentative evidence. Finally, we discuss that translational invariance in a quantum system at zero temperature, size goes to infinity and no mass scales, except for cut‐off, possibly be a necessary condition in quantum gravity theory by ruing out a volume law of entanglement entropy. The subject of this article is the entanglement entropy in gravity theory with quantum effects. A simple model is a two dimensional Einstein gravity theory using an n‐sheet manifold to obtain an area term of entanglement entropy by summing over all background fields. Based on AdS/CFT correspondence, strongly coupled conformal field theory is expected to describe perturbative quantum gravity theory. An ultraviolet complete quantum gravity theory should not depend on a choice of an entangling surface. Using two dimensional conformal field theory the author finds that a coefficient of a universal term of entanglement entropy is independent of the choice of the entangling surface in two dimensional conformal field theory.