Left-Right Entanglement Entropy of Boundary States

TL;DR

This work analyzes left-right entanglement entropy in boundary conformal field theories by tracing over one chiral sector of boundary states for both free and compact bosons. The authors regularize boundary states with a small parameter ε, compute the reduced density matrix ρ_A = Tr_B ρ, and derive entanglement and Rényi entropies that reveal a thermal CFT gas interpretation with a leading term S_A ∝ π/(24 ε). In the compact case, they obtain radius-dependent corrections, showing compatibility with T-duality under R → 2/R. The results unify BCFT boundary-state entanglement with thermal behavior and string-theory boundary states, suggesting possible universal features for BCFT entanglement and providing groundwork for extensions to more general boundary conditions and D-brane configurations.

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.