Left-Right Entanglement Entropy of Boundary States

TL;DR

This paper analyzes the entanglement entropy of boundary states in free bosonic conformal field theories, revealing that the reduced system behaves like a thermal CFT gas and confirming T-duality consistency.

Contribution

It provides a detailed calculation of entanglement entropy for boundary states, extending previous quantum mechanics and field theory results to include compact and noncompact bosons.

Findings

Reduced density matrix resembles a thermal CFT gas

Results are consistent with T-duality in compact cases

Generalizes known quantum entanglement results

Abstract

We study entanglement entropy of boundary states in a free bosonic conformal field theory. A boundary state can be thought of as composed of a particular combination of left and right-moving modes of the two-dimensional conformal field theory. We investigate the reduced density matrix obtained by tracing over the right-moving modes in various boundary states. We consider Dirichlet and Neumann boundary states of a free noncompact as well as a compact boson. The results for the entanglement entropy indicate that the reduced system can be viewed as a thermal CFT gas. Our findings are in agreement and generalize results in quantum mechanics and quantum field theory where coherent states can also be considered. In the compact case we verify that the entanglement entropy expressions are consistent with T-duality.