Discussion of Entanglement Entropy in Quantum Gravity

作者：Ma Chen Te^*

来源：Progress of Physics, 2018, 66(2): 1700095.

DOI：10.1002/prop.201700095

• conformal field theory
• models of quantum gravity
• topological field theories

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.

• 出版日期2018-2