# Relating bulk to boundary entanglement

## TL;DR

This paper explores the relationship between bulk and boundary entanglement entropy in quantum field theories with boundaries, revealing universal connections and proposing models that simplify entanglement calculations.

## Contribution

It establishes a universal relation between bulk and boundary entanglement entropy terms across various dimensions and theories, and introduces the boundary Extensive Mutual Information model.

## Key findings

- Universal boundary-bulk entanglement relation in CFTs and Lifshitz theories
- Corner-induced logarithmic terms relate to boundary effects in 2+1 dimensions
- Numerical validation with lattice models and boundary conditions

## Abstract

Quantum many-body systems have a rich structure in the presence of boundaries. We study the groundstates of conformal field theories (CFTs) and Lifshitz field theories in the presence of a boundary through the lens of the entanglement entropy. For a family of theories in general dimensions, we relate the universal terms in the entanglement entropy of the bulk theory with the corresponding terms for the theory with a boundary. This relation imposes a condition on certain boundary central charges. For example, in $2+1$ dimensions, we show that the corner-induced logarithmic terms of free CFTs and certain Lifshitz theories are simply related to those that arise when the corner touches the boundary. We test our findings on the lattice, including a numerical implementation of Neumann boundary conditions. We also propose an ansatz, the boundary Extensive Mutual Information model, for a CFT with a boundary whose entanglement entropy is purely geometrical. This model shows the same bulk-boundary connection as Dirac fermions and certain supersymmetric CFTs that have a holographic dual. Finally, we discuss how our results can be generalized to all dimensions as well as to massive quantum field theories.