Universal features of left-right entanglement entropy

TL;DR

This paper uncovers universal features in the entanglement entropy of boundary states in 1+1D conformal field theories, linking it to topological quantum field theories and deriving a general formula involving the central charge and modular S matrix.

Contribution

It introduces a universal formula for left-right entanglement entropy in 1+1D CFTs and connects it to spatial entanglement in 2+1D topological theories, with explicit examples.

Findings

Universal entanglement features depend on central charge and modular S matrix.

Left-right entanglement entropy reproduces spatial entanglement in topological QFTs.

Explicit calculations for Ising, tricritical Ising, and su(2)_k WZW models.

Abstract

We show the presence of universal features in the entanglement entropy of regularized boundary states for (1+1)-d conformal field theories on a circle when the reduced density matrix is obtained by tracing over right/left-moving modes. We derive a general formula for the left-right entanglement entropy in terms of the central charge and the modular S matrix of the theory. When the state is chosen to be an Ishibashi state, this measure of entanglement is shown to reproduce the spatial entanglement entropy of a (2+1)-d topological quantum field theory. We explicitly evaluate the left-right entanglement entropies for the Ising model, the tricritical Ising model and the su(2)_k WZW model as examples.